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Within the 9th European Framework programme, since 2021 EUROfusion is operating five tokamaks under the auspices of a single Task Force called ‘Tokamak Exploitation’. The goal is to benefit from the complementary capabilities of each machine in a coordinated way and help in developing a scientific output scalable to future largre machines. The programme of this Task Force ensures that ASDEX Upgrade, MAST-U, TCV, WEST and JET (since 2022) work together to achieve the objectives of Missions 1 and 2 of the EUROfusion Roadmap: i) demonstrate plasma scenarios that increase the success margin of ITER and satisfy the requirements of DEMO and, ii) demonstrate an integrated approach that can handle the large power leaving ITER and DEMO plasmas. The Tokamak Exploitation task force has therefore organized experiments on these two missions with the goal to strengthen the physics and operational basis for the ITER baseline scenario and for exploiting the recent plasma exhaust enhancements in all four devices (PEX: Plasma EXhaust) for exploring the solution for handling heat and particle exhaust in ITER and develop the conceptual solutions for DEMO. The ITER Baseline scenario has been developed in a similar way in ASDEX Upgrade, TCV and JET. Key risks for ITER such as disruptions and run-aways have been also investigated in TCV, ASDEX Upgrade and JET. Experiments have explored successfully different divertor configurations (standard, super-X, snowflakes) in MAST-U and TCV and studied tungsten melting in WEST and ASDEX Upgrade. The input from the smaller devices to JET has also been proven successful to set-up novel control schemes on disruption avoidance and detachment.

Telomere maintenance 2 (TELO2), Tel2 interacting protein 2 (TTI2), and Tel2 interacting protein 1 (TTI1) are the three components of the conserved Triple T (TTT) complex that modulates activity of phosphatidylinositol 3-kinase-related protein kinases (PIKKs), including mTOR, ATM, and ATR, by regulating the assembly of mTOR complex 1 (mTORC1). The TTT complex is essential for the expression, maturation, and stability of ATM and ATR in response to DNA damage. TELO2- and TTI2-related bi-allelic autosomal-recessive (AR) encephalopathies have been described in individuals with moderate to severe intellectual disability (ID), short stature, postnatal microcephaly, and a movement disorder (in the case of variants within TELO2). We present clinical, genomic, and functional data from 11 individuals in 9 unrelated families with bi-allelic variants in TTI1. All present with ID, and most with microcephaly, short stature, and a movement disorder. Functional studies performed in HEK293T cell lines and fibroblasts and lymphoblastoid cells derived from 4 unrelated individuals showed impairment of the TTT complex and of mTOR pathway activity which is improved by treatment with Rapamycin. Our data delineate a TTI1-related neurodevelopmental disorder and expand the group of disorders related to the TTT complex. © 2023 American Society of Human Genetics

Family Puzzle or Generation Problem demands an explanation of why there are 3 families or generations of quarks and leptons in the Standard Model of particle physics. Here we propose a novel solution -- the multiple of 3 families of 16 Weyl fermions (namely $(N_f=3) \times 16$) in the 3+1d spacetime dimensions are topologically robust due to constraints rooted in profound mathematics (such as Hirzebruch signature and Rokhlin theorems, and cobordism) and derivable in physics (such as chiral edge states, quantized thermal Hall conductance, and gravitational Chern-Simons theory), which holds true even forgetting or getting rid of any global symmetry or gauge structure of the Standard Model. By the dimensional reduction through a sequence of sign-reversing mass domain wall of domain wall and so on, we reduce the Standard Model fermions to obtain the $(N_f=3) \times 16$ multiple of 1+1d Majorana-Weyl fermion with a total chiral central charge $c_-=24$. Effectively via the fermionization-bosonization, the 1+1d theory becomes 3 copies of $c_-=8$ of (E$_8)_1$ conformal field theory, living on the boundary of 3 copies of 2+1d E$_8$ quantum Hall states. Based on the framing anomaly-free $c_- = 0 \mod 24$ modular invariance, the framed bordism and string bordism $\mathbb{Z}_{24}$ class, the 2-framing and $p_1$-structure, the $w_1$-$p_1$ bordism $\mathbb{Z}_3$ class constraints, we derive the family number constraint $N_f \in (\frac{48}{16} =\frac{24}{8}=3) \mathbb{Z}$. The dimensional reduction process, although not necessary, is sufficiently supported by the $\mathbb{Z}_{16}$ class Smith homomorphism. We also comment on the $\frac{45}{15}=3$ relation: the 3 families of 15 Weyl-fermion Standard Model vacuum where the absence of some sterile right-handed neutrinos is fulfilled by additional topological field theories or conformal field theories in Ultra Unification.

Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity $(-1)^{\rm F}$ are basic discrete spacetime and internal symmetries of the Dirac fermions. In this article, we determine the group, called the C-R-T fractionalization, which is a group extension of $\mathbb{Z}_2^{\rm C}\times\mathbb{Z}_2^{\rm R}\times\mathbb{Z}_2^{\rm T}$ by the fermion parity $\mathbb{Z}_2^{\rm F}$, and its extension class in all spacetime dimensions $d$, for a single-particle fermion theory. For Dirac fermions, with the canonical CRT symmetry $\mathbb{Z}_2^{\rm CRT}$, the C-R-T fractionalization has two possibilities that only depend on spacetime dimensions $d$ modulo 8, which are order-16 nonabelian groups, including the famous Pauli group. For Majorana fermions, we determine the R-T fractionalization in all spacetime dimensions $d=0,1,2,3,4\mod8$, which is an order-8 abelian or nonabelian group. For Weyl fermions, we determine the C or T fractionalization in all even spacetime dimensions $d$, which is an order-4 abelian group. For Majorana-Weyl fermions, we only have an order-2 $\mathbb{Z}_2^{\rm F}$ group. We discuss how the Dirac and Majorana mass terms break the symmetries C, R, or T. We study the domain wall dimensional reduction of the fermions and their C-R-T fractionalization: from $d$-dim Dirac to $(d-1)$-dim Dirac or Weyl; and from $d$-dim Majorana to $(d-1)$-dim Majorana or Majorana-Weyl., Comment: 39 pages, 5 figures, 17 tables, see C-P-T fractionalization in arXiv:2109.15320, and an application of domain wall dimensional reduction in arXiv:2312.14928

Family Puzzle or Generation Problem demands an explanation of why there are 3 families or generations of quarks and leptons in the Standard Model of particle physics. Here we propose a novel solution -- the multiple of 3 families of 16 Weyl fermions (namely $(N_f=3) \times 16$) in the 3+1d spacetime dimensions are topologically robust due to constraints rooted in profound mathematics (such as Hirzebruch signature and Rokhlin theorems, and cobordism) and derivable in physics (such as chiral edge states, quantized thermal Hall conductance, and gravitational Chern-Simons theory), which holds true even forgetting or getting rid of any global symmetry or gauge structure of the Standard Model. By the dimensional reduction through a sequence of sign-reversing mass domain wall of domain wall and so on, we reduce the Standard Model fermions to obtain the $(N_f=3) \times 16$ multiple of 1+1d Majorana-Weyl fermion with a total chiral central charge $c_-=24$. Effectively via the fermionization-bosonization, the 1+1d theory becomes 3 copies of $c_-=8$ of (E$_8)_1$ conformal field theory, living on the boundary of 3 copies of 2+1d E$_8$ quantum Hall states. Based on the framing anomaly-free $c_- = 0 \mod 24$ modular invariance, the framed bordism and string bordism $\mathbb{Z}_{24}$ class, the 2-framing and $p_1$-structure, the $w_1$-$p_1$ bordism $\mathbb{Z}_3$ class constraints, we derive the family number constraint $N_f \in (\frac{48}{16} =\frac{24}{8}=3) \mathbb{Z}$. The dimensional reduction process, although not necessary, is sufficiently supported by the $\mathbb{Z}_{16}$ class Smith homomorphism. We also comment on the $\frac{45}{15}=3$ relation: the 3 families of 15 Weyl-fermion Standard Model vacuum where the absence of some sterile right-handed neutrinos is fulfilled by additional topological field theories or conformal field theories in Ultra Unification.

Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity $(-1)^{\rm F}$ are basic discrete spacetime and internal symmetries of the Dirac fermions. In this article, we determine the group, called the C-R-T fractionalization, which is a group extension of $\mathbb{Z}_2^{\rm C}\times\mathbb{Z}_2^{\rm R}\times\mathbb{Z}_2^{\rm T}$ by the fermion parity $\mathbb{Z}_2^{\rm F}$, and its extension class in all spacetime dimensions $d$, for a single-particle fermion theory. For Dirac fermions, with the canonical CRT symmetry $\mathbb{Z}_2^{\rm CRT}$, the C-R-T fractionalization has two possibilities that only depend on spacetime dimensions $d$ modulo 8, which are order-16 nonabelian groups, including the famous Pauli group. For Majorana fermions, we determine the R-T fractionalization in all spacetime dimensions $d=0,1,2,3,4\mod8$, which is an order-8 abelian or nonabelian group. For Weyl fermions, we determine the C or T fractionalization in all even spacetime dimensions $d$, which is an order-4 abelian group. For Majorana-Weyl fermions, we only have an order-2 $\mathbb{Z}_2^{\rm F}$ group. We discuss how the Dirac and Majorana mass terms break the symmetries C, R, or T. We study the domain wall dimensional reduction of the fermions and their C-R-T fractionalization: from $d$-dim Dirac to $(d-1)$-dim Dirac or Weyl; and from $d$-dim Majorana to $(d-1)$-dim Majorana or Majorana-Weyl., Comment: 39 pages, 5 figures, 17 tables, see C-P-T fractionalization in arXiv:2109.15320, and an application of domain wall dimensional reduction in arXiv:2312.14928

In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf L$ number symmetry is free of mixed anomalies with strong and electroweak $su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces. However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent to leptogenesis in the very early universe. This happens when the total "sterile right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number $N_f$. Thus the invertible $\bf B - L$ symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical $\bf B - L$ generalized symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by $\mathbb{Z}$ and $\mathbb{Z}_{16}$ respectively. For this construction, we utilize the anomaly inflow bulk-boundary correspondence, the 4d Pontryagin class and the gravitational Chern-Simons 3-form, the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate rational chiral central charge, and the 4d $\mathbb{Z}_4^{\rm TF}$-time-reversal symmetric topological superconductor with 3d boundary topological order., Comment: 34 pages. v2: refinements with new tables and appendices, including discussions on Atiyah's 2-framing and $p_1$ structures

We propose that the Fermi surface anomaly of symmetry group $G$ in any dimension is universally classified by $G$-symmetric interacting fermionic symmetry-protected topological (SPT) phases in $(0+1)$-dimensional spacetime. The argument is based on the perspective that the gapless fermions on the Fermi surface can be viewed as the topological boundary modes of Chern insulators in the phase space (position-momentum space). Given the non-commutative nature of the phase space coordinates, we show that the momentum space dimensions should be counted as negative dimensions for SPT classification purposes. Therefore, the classification of phase-space Chern insulators (or, more generally fermionic SPT phases) always reduces to a $(0+1)$-dimensional problem, which can then be answered by the cobordism approach. In addition to the codimension-1 Fermi surface case, we also discuss the codimension-$p$ Fermi surface case briefly. We provide concrete examples to demonstrate the validity of our classification scheme, and make connections to the recent development of Fermi surface symmetric mass generation., Comment: 13 pages + references, 2 figures, 2 tables. Update Tab. II, clarifications to codimension-p Fermi surface, and references added

In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf L$ number symmetry is free of mixed anomalies with strong and electroweak $su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces. However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent to leptogenesis in the very early universe. This happens when the total "sterile right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number $N_f$. Thus the invertible $\bf B - L$ symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical $\bf B - L$ generalized symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by $\mathbb{Z}$ and $\mathbb{Z}_{16}$ respectively. For this construction, we utilize the anomaly inflow bulk-boundary correspondence, the 4d Pontryagin class and the gravitational Chern-Simons 3-form, the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate rational chiral central charge, and the 4d $\mathbb{Z}_4^{\rm TF}$-time-reversal symmetric topological superconductor with 3d boundary topological order., Comment: 34 pages. v2: refinements with new tables and appendices, including discussions on Atiyah's 2-framing and $p_1$ structures

Family Puzzle or Generation Problem demands an explanation of why there are 3 families or generations of quarks and leptons in the Standard Model of particle physics. Here we propose a novel solution -- the multiple of 3 families of 16 Weyl fermions (namely $(N_f=3) \times 16$) in the 3+1d spacetime dimensions are topologically robust due to constraints rooted in profound mathematics (such as Hirzebruch signature and Rokhlin theorems, and cobordism) and derivable in physics (such as chiral edge states, quantized thermal Hall conductance, and gravitational Chern-Simons theory), which holds true even forgetting or getting rid of any global symmetry or gauge structure of the Standard Model. By the dimensional reduction through a sequence of sign-reversing mass domain wall of domain wall and so on, we reduce the Standard Model fermions to obtain the $(N_f=3) \times 16$ multiple of 1+1d Majorana-Weyl fermion with a total chiral central charge $c_-=24$. Effectively via the fermionization-bosonization, the 1+1d theory becomes 3 copies of $c_-=8$ of (E$_8)_1$ conformal field theory, living on the boundary of 3 copies of 2+1d E$_8$ quantum Hall states. Based on the framing anomaly-free $c_- = 0 \mod 24$ modular invariance, the framed bordism and string bordism $\mathbb{Z}_{24}$ class, the 2-framing and $p_1$-structure, the $w_1$-$p_1$ bordism $\mathbb{Z}_3$ class constraints, we derive the family number constraint $N_f \in (\frac{48}{16} =\frac{24}{8}=3) \mathbb{Z}$. The dimensional reduction process, although not necessary, is sufficiently supported by the $\mathbb{Z}_{16}$ class Smith homomorphism. We also comment on the $\frac{45}{15}=3$ relation: the 3 families of 15 Weyl-fermion Standard Model vacuum where the absence of some sterile right-handed neutrinos is fulfilled by additional topological field theories or conformal field theories in Ultra Unification.

The objective of the study was to determine if there is a significant correlation between collaborative learning and teaching performance. For this reason, research on collaborative learning was carried out to improve teaching performance in higher education. The type of research is applied, with the level of research being descriptive and correlational. The research was transversal; since the survey was carried out only once using the questionnaire and notes technique. The sample is simple random, 54 enrolled students, who constitute the study of Professional Schools of Mechanical and Electrical Engineering at the National Technological University of Lima Sur. It is shown that of the total number of respondents (the high level predominates), that is, represented by 61.11% (33) perceive collaborative learning, 38.89% (21) at the medium level. The average of those surveyed in the collaborative learning application is favorable. The most repeated value being 3 (favorable). More than 50% of the respondents are above 3.0370, that is, they have a favorable attitude. On average, the subjects are located at 3.0000 (favorable). Likewise, 1.14863 scale units deviate from the average. Finally, it is concluded that there is an adequate significant relationship between the variables, due to a moderate correlation of 00.548, that is, it is favorable., El estudio tuvo como objetivo determinar si existe correlación significativa entre aprendizajes colaborativo y el desempeño docente. Por este motivo, se realizó la investigación sobre aprendizajes colaborativo para mejorar el desempeño docente en la educación superior. El tipo de investigación es aplicada, siendo el nivel de investigación descriptiva y correlacional. La investigación fue transversal; puesto que se realizó una sola vez la encuesta mediante la técnica del cuestionario y notas. La muestra es aleatoria simple  54 estudiantes matriculados, que constituyen el estudio de Escuelas Profesionales de Ingeniería Mecánica  y Eléctrica de la Universidad Nacional Tecnológica de Lima Sur. Se demuestra que del total de los encuestados (predomina el nivel alto), es decir, representada por el 61,11 % (33) percibe el aprendizaje colaborativo ocupa, el 38,89% (21) en el nivel medio. El promedio de los encuestados en la aplicación aprendizajes colaborativo es favorable. Siendo el valor que más se repite 3 (favorable). Más del 50% de los encuestados están por encima de 3,0370, es decir, tienen una actitud favorable. En promedio los sujetos se ubican en 3,0000 (favorable). Asimismo, se desvían con respecto al promedio 1,14863 unidades de la escala. Por último, se concluye que sí existe una adecuada relación significativa entre las variables, debido a una correlación moderada de 00,548, es decir es favorable.

Research is a transversal axis in the curriculum of future professionals, therefore, the university has to promote research to help solve the different problems of society. The study had as objective to determine what are the attitudes towards research in students of some public universities. Basic research of non-experimental design carried out on 183 students from the Santiago Antúnez de Mayolo National University, the National University of San Marcos and the National University of Engineering. Data were collected through a questionnaire on attitudes towards research applied online and statistical analysis was performed with the non-parametric Kruskal-Wallis and Mann-Whitney U test. The results show that the students of the National Engineering University present a higher score (Mdn=92; Rank=61) regarding the attitude towards research, followed by the students of the National University of San Marcos (Mdn=89; Rank=63) and of the students of the Santiago Antúnez de Mayolo National University (Mdn=86; Rank=58). It is concluded that there are significant differences in the attitude towards research in the students of the universities under study., La investigación es un eje transversal en el currículo de los futuros profesionales, por lo tanto, la universidad tiene que promover la investigación para ayudar a solucionar los distintos problemas de la sociedad. El estudio tuvo como objetivo determinar cuál son las actitudes hacia la investigación en estudiantes de algunas universidades públicas. Investigación básica de diseño no experimental realizado en 183 estudiantes de la Universidad Nacional Santiago Antúnez de Mayolo, Universidad Nacional Mayor de San Marcos y la Universidad Nacional de Ingeniería. Los datos se recolectaron mediante un cuestionario de actitudes hacia la investigación aplicado vía online y el análisis estadístico se realizó con la prueba no paramétrica de Kruskal-Wallis y U de Mann-Whitney. En los resultados se aprecia que los estudiantes de la Universidad Nacional de Ingeniería presentan una puntuación (Mdn=92; Rango=61) más alta con respecto a la actitud hacia la investigación, seguidos de los estudiantes de la Universidad Nacional Mayor de San Marcos (Mdn=89; Rango=63) y de los estudiantes de la Universidad Nacional Santiago Antúnez de Mayolo (Mdn=86; Rango= 58). Se concluye que existen diferencias significativas en la actitud hacia a la investigación en los estudiantes de las universidades en estudio.

Introduction Attendance plays a pivotal role in a student's academic success, as it optimizes the learning opportunities available during school hours. The act of attending classes contributes significantly to the acquisition of knowledge. However, the issue of tardiness has historically plagued educational institutions, presenting a formidable obstacle for students by causing them to miss valuable class time and subsequently fall behind in their studies. This phenomenon has led to a cascade of challenges, including difficulties in catching up with missed lessons and educators grappling with the task of helping students bridge the knowledge gap. At Union Christian College, the normalization and persistence of tardiness among certain students have been notable, often resulting in their referral to the guidance office. Seeking to comprehend the underlying causes of this tardiness, a comprehensive study was undertaken by the researchers. The primary objective of this study was to identify the perceived triggers behind junior high school students' chronic tardiness. Method To fulfil this aim, a descriptive-survey design was adopted to outline the perceived factors contributing to their consistent lateness. Data collection encompassed the administration of a modified questionnaire to a cohort of 30 Junior High School Students from Union Christian College. Utilizing frequency counts and percentages, the students' profiles and the extent of their tardiness were delineated. Additionally, the researchers employed the weighted mean to present the factors believed to be responsible for the students' habitual lateness. Results and Discussion The findings of the study revealed that most respondents were male and around 15 years old. Regarding the frequency of tardiness, most students reported being late to school between 1 to 4 times in the preceding three quarters of the academic year. Although not considered severe, this recurring pattern underscored the need for intervent

Introduction Attendance plays a pivotal role in a student's academic success, as it optimizes the learning opportunities available during school hours. The act of attending classes contributes significantly to the acquisition of knowledge. However, the issue of tardiness has historically plagued educational institutions, presenting a formidable obstacle for students by causing them to miss valuable class time and subsequently fall behind in their studies. This phenomenon has led to a cascade of challenges, including difficulties in catching up with missed lessons and educators grappling with the task of helping students bridge the knowledge gap. At Union Christian College, the normalization and persistence of tardiness among certain students have been notable, often resulting in their referral to the guidance office. Seeking to comprehend the underlying causes of this tardiness, a comprehensive study was undertaken by the researchers. The primary objective of this study was to identify the perceived triggers behind junior high school students' chronic tardiness. Method To fulfil this aim, a descriptive-survey design was adopted to outline the perceived factors contributing to their consistent lateness. Data collection encompassed the administration of a modified questionnaire to a cohort of 30 Junior High School Students from Union Christian College. Utilizing frequency counts and percentages, the students' profiles and the extent of their tardiness were delineated. Additionally, the researchers employed the weighted mean to present the factors believed to be responsible for the students' habitual lateness. Results and Discussion The findings of the study revealed that most respondents were male and around 15 years old. Regarding the frequency of tardiness, most students reported being late to school between 1 to 4 times in the preceding three quarters of the academic year. Although not considered severe, this recurring pattern underscored the need for intervent

The study aimed to determine if there is a significant relationship between multiple intelligence and learning. For this reason, the research was carried out in higher education. The type of research is applied, being the level of descriptive and correlational research. The research was cross-sectional; since the survey was carried out only once using the technique of the questionnaire and notes. The sample is simple random 48 students. Naturalistic intelligence was shown to be at the highest level of 3.3750; while interpersonal and emotional is 3.3125, musical is 3.2917; and the lowest is Kinesthetic-Corporal is 3.0833 and the general average is 3.2176. Therefore, multiple intelligences improve student learning; however, it is necessary that teachers take into account in their classes the naturalistic, interpersonal and emotional intelligences are the most representative. It was determined that more than 50% of the respondents are located at 3,0000, since the maximum is five, then it is favorable. Likewise, the most repeated times is 3.00 Likewise, 1.14854 scale units deviate from the average, because it is low it induces less data dispersion. Therefore, it is used in learning the multiple intelligences of the students. Finally, the calculated p value is 0.000, which is less than 0.01 (0.000< 0.001), so the null hypothesis is rejected and the alternative hypothesis is accepted. The rho coefficient is 0.852, which indicates that the relationship between the variables is direct and its degree is very high. In conclusion: It can be stated with 99% confidence that there is a very high positive relationship between the degree of multiple intelligences and the learning of university students., El estudio tuvo como objetivo determinar si existe relación significativa entre la inteligencia múltiple y el aprendizaje. Por este motivo, se realizó la investigación en la educación superior. El tipo de investigación es aplicada, siendo el nivel de investigación descriptiva y correlacional. La investigación fue transversal; puesto que se realizó una sola vez la encuesta mediante la técnica del cuestionario y notas. La muestra es aleatoria simple 48 estudiantes. Se demostró que la inteligencia naturalista en el nivel más alto de 3,3750; mientras interpersonal y emocional es 3,3125, musical es 3,2917; y el más bajo es Kinestésico-Corporal es 3,0833 y el promedio general es 3,2176. Por lo tanto, las inteligencias múltiples mejora en el aprendizaje de los estudiantes; sin embargo, es necesario que los docentes tomen en cuenta en sus clases las inteligencias naturalista, interpersonal y emocional son las más representativa. Se determinó que más del 50% de los encuestados se ubican en 3, 0000, ya que el máximo es cinco, entonces es favorable. Asimismo, las veces que más se repite es 3,00 Asimismo, se desvían con respecto al promedio 1,14854 unidades de la escala, debido a que es bajo induce una menor dispersión de datos. Por lo tanto, que es empleado en el aprendizaje las inteligencias múltiples de los estudiantes. Por último, el p valor calculado es de 0.000, que es menor al 0.01 (0.000< 0.001), por lo que se rechaza la hipótesis nula y se acepta la hipótesis alterna. El coeficiente rho es 0,852, lo que indica que la relación entre las variables es directa y su grado es muy alta. En conclusión: Se puede afirmar con un 99% de confianza que existe una relación positiva muy alta entre el grado de inteligencias múltiples y el aprendizaje de los universitarios.

The objective of the study was to determine if there is a significant correlation between the use of ICT tools and academic performance. For this reason, research on the use of ICT tools to improve academic performance in higher education was carried out. The type of research is applied, being the level of descriptive and correlational research. The research was cross-sectional; since the survey was carried out only once using the technique of the questionnaire and notes. The sample is simple random 57 students enrolled in the 2023 semester, which constitute the study. It is shown that of the total number of respondents, the medium level predominates, that is, represented by 34.0% (59.65) perceives that the use of ICT tools occupies, 22.81% (13) at the high level. The average of those surveyed towards the application of the use of ICT tools is favorable. Being the most repeated value 3 (favorable). More than 50% of those surveyed are above 2.9474, that is, they have a favorable attitude. On average the subjects are located at 3.0000 (favorable). Likewise, 1.27365 scale units deviate from the average. A minimum score of 1 and a maximum of 5 was observed. Finally, it is concluded that there is an adequate significant relationship between the use of ICT and the academic performance of university students, due to a moderate correlation of 0.785., El estudio tuvo como objetivo determinar si existe correlación significativa entre Uso de herramientas TIC y rendimiento académico. Por este motivo, se realizó la investigación sobre Uso de herramientas TIC para mejorar el rendimiento académico en la educación superior. El tipo de investigación es aplicada, siendo el nivel de investigación descriptiva y correlacional. La investigación fue transversal; puesto que se realizó una sola vez la encuesta mediante la técnica del cuestionario y notas. La muestra es aleatoria simple, 57 estudiantes matriculados en el semestre 2023, que constituyen el estudio. Se demuestra que del total de los encuestados predomina el nivel el medio, es decir, representada por el 34,0% (59,65) percibe que uso de las herramientas TIC ocupa, el 22,81% (13) en el nivel alto.  El promedio de los encuestados hacia la aplicación uso de herramientas TIC es favorable. Siendo el valor que más se repite 3 (favorable). Más del 50% de los encuestados están por encima de 2,9474, es decir, tienen una actitud favorable. En promedio los sujetos se ubican en 3,0000 (favorable). Asimismo, se desvían con respecto al promedio 1,27365 unidades de la escala. Se observó un puntaje mínimo alcanzado de 1 y el máximo de 5. Por último, se concluye que sí existe una adecuada relación significativa entre el uso de TIC y el rendimiento académico de los universitarios, debido a una correlación moderada de 0,785.

The objective of the study was to determine if there is a significant correlation between teamwork and academic performance. For this reason, research on teamwork to improve academic performance in higher education was carried out. The type of research is applied, being the level of descriptive and correlational research. The research was cross-sectional; since the survey was carried out only once using the questionnaire technique, the Likert Scale and notes. The sample is simple random 41 students enrolled in the 2022-1 semester, which constitute the study of the Professional School of Accounting-UNDC. It is shown that of the total number of respondents (the medium level predominates, that is, represented by 39.0% (16) perceives that the application of teamwork occupies 61.0% (25) at the highest level More than 50% of those surveyed are above 2.61, that is, they have a favorable attitude.The average of those surveyed is located at 2.61 (favorable).In addition, they deviate from the average by 0.494 units on the scale Finally, it is concluded that there is an adequate significant relationship between the variables, due to a moderate correlation of 0.738, that is, it is favorable., El estudio tuvo como objetivo determinar si existe correlación significativa entre el trabajo en equipo y el rendimiento académico. Por este motivo, se realizó la investigación sobre el trabajo en equipo para mejorar el rendimiento académico en la educación superior. El tipo de investigación es aplicada, siendo el nivel de investigación descriptiva y correlacional. La investigación fue transversal; puesto que se realizó una sola vez la encuesta mediante la técnica del cuestionario la Escala de Likert y notas. La muestra es aleatoria simple 41 estudiantes matriculados en el semestre 2022-1, que constituyen el estudio de la Escuela Profesional de Contabilidad-UNDC. Se demuestra que del total de los encuestados (predomina el nivel medio, es decir, representada por el 39,0% (16) percibe que la aplicación del trabajo en equipo ocupa, el 61,0% (25) en el nivel más alto. Más del 50% de los encuestados están por encima de 2.61, es decir, tienen una actitud favorable. En promedio de los encuestados se ubican en 2,61 (favorable). Asimismo, se desvían con respecto al promedio 0,494 unidades de la escala. Por último, se concluye que sí existe una adecuada relación significativa entre las variables, debido a una correlación moderada de 0,738, es decir es favorable.

The study aimed to determine if there is a significant relationship between self-esteem and academic performance. For this reason, research on self-esteem was carried out to improve academic performance in higher education. The type of research is applied, being the level of descriptive and correlational research. The research was cross-sectional, since the survey was carried out only once using the technique of the questionnaire and notes. The sample is simple random 56 students. It was shown that emotional and personal self-esteem occupies 64.3% (36) at the highest level; 21.4% (12) represent family self-esteem; 14.3% (8) is the minimum of the study. Therefore, self-esteem improves in the academic performance of students; however, it is necessary that teachers consider emotional and personal self-esteem in their classes. It was determined that more than 50% of the respondents are above 2.00, that is, they have a favorable attitude. On average, the subjects are located at 1.93 (favorable). Likewise, 0.599 scale units deviate from the average. Therefore, self-esteem benefits the student. Finally, it is concluded that there is an adequate significant relationship between self-esteem and the academic performance of university students, since 9.4877 > 4.445a; then, the null hypothesis is accepted and the alternative hypothesis is rejected, that is, it is favorable.

The objective of the study was to determine if there is a significant correlation between academic motivation and student learning. For this reason, research on academic motivation was carried out to improve the teaching and learning of university students. The study carried out is applied, being the level of descriptive-correlational research. The research was cross-sectional; since the CEAP48 Scale survey was applied only once; but only the EMAP-01 Learning Motivation Subscale was used, which consists of 24 statements and notes. The sample is a simple random of 46 students enrolled in the 2022-1 semester. It was shown that the application of academic motivation and learning occupies 71.7% (33) at the highest level in the performance motivation dimension. Therefore, motivation improves in learning; however, it is necessary for teachers to apply this didactic resource in their classes, since it is demonstrated in the results. It was determined that more than 50% of the respondents are above 3.96 in the mean, that is, they have a favorable attitude. On average, the subjects are located in superficial motivation. Likewise, 0.631 scale units deviate from the average. Therefore, the use of this resource benefits the student. Finally, it is concluded that there is an adequate significant relationship between the variables, due to a moderate correlation, that is, it is favorable., El estudio tuvo como objetivo determinar si existe correlación significativa entre la motivación académica y el aprendizaje de los estudiantes. Por este motivo, se realizó la investigación sobre la motivación académica para mejorar la enseñanza y aprendizaje de los universitarios. El estudio es aplicado, siendo el nivel de investigación descriptiva- correlacional. La investigación fue transversal; puesto que se aplicó una sola vez la encuesta de la Escala el CEAP48; pero solo se empleó la EMAP-01 Subescala de Motivación al aprendizaje, que consta de 24 afirmaciones y notas. La muestra es aleatoria simple de 46 estudiantes matriculados en el semestre 2022-1. Se demostró que la aplicación la motivación académico y aprendizaje ocupa, el 71,7% (33) en el nivel más alto en la dimensión motivación rendimiento. Por lo tanto, la motivación mejora en el aprendizaje; sin embargo, es necesario que los docentes apliquen en sus clases este recurso didáctico, ya que está demostrado en los resultados. Se determinó que más del 50% de los encuestados están por encima de 3.96 en la media, es decir, tienen una actitud favorable. En promedio los sujetos se ubican en la motivación superficial. Asimismo, se desvían con respecto al promedio 0,631 unidades de la escala. Por lo tanto, el uso de este recurso beneficia al estudiante. Por último, se concluye que sí existe una adecuada relación significativa entre las variables, debido a una correlación moderada, es decir es favorable.

We present a model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement (namely confinement without chiral symmetry breaking in a supersymmetric gauge theory) at an intermediate energy scale, before the electroweak symmetry breaking by the Higgs condensation at lower energy. In our context, the smooth confinement preserves the SU(3) and the chiral SU(2)$_L\times$ U(1)$_Y$ symmetry in a supersymmetric Standard Model, while this internal symmetry becomes dynamically gauged in the end. In contrast to Razamat-Tong's symmetric mass generation model also preserving the $G_{\rm SM} \equiv$ SU(3)$_C\times$ SU(2)$_L\times$ U(1)$_Y$ internal symmetry, our model introduces different matter contents with a different kind of superpotential deformation irrelevant at UV, which further induces Yukawa-Higgs terms marginal at IR, breaking the $G_{\rm SM}$ down to SU(3)$_C$ and the electromagnetic U(1)$_{\rm EM}$ only when Higgs condenses. In our model, the IR fermions in the first and second families are composite of UV fields, while the third family elementary fermions match between UV and IR. The smallness of the first and second family fermion masses is explained by the exponential hierarchy between the cutoff scale and the smooth confinement scale via dimensional transmutation. As a result, our UV Lagrangian only contains the natural parameters close to the order one., Comment: 11 pages, 1 figure (v1); references add, modifications for clarity (v2); matches published version (v3)

El segundo número de la colección Laboratorio Transmedia (ISSN: 2794-0861) contiene 36 relatos escritos durante el curso 2021/2022 por estudiantes de la Universidad para Mayores.

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG., Comment: 33 pages. An invited overview of Symmetric Mass Generation. Introduce a novel unifying theoretical framework. We thank Cenke Xu for initiating this project

A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamical SM gauge field, it is important to check whether they have mixed anomalies with the gravitational background field and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of discrete ${\bf B + L}$ symmetry protection, in particular (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry with the fermion parity $\mathbb{Z}_2^{\rm F}$., Comment: 6 pages. Sequel to arXiv:2112.14765. v2: refinement. Related talks: https://www.youtube.com/results?search_query=cobordism+deformation+standard+model+crticiality. The original title "Proton Stability: From the Standard Model to Ultra Unification" is adjusted in PRD

For the 4d Standard Model (SM) with Lie group $G_{{\rm SM}_q} \equiv$ SU(3)$\times$SU(2)$\times$U(1)$_{\tilde Y}/\mathbb{Z}_q$ of $q=1,2,3,6$ with $N_f$ family of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamically gauged $G_{{\rm SM}_q}$, it is important to check whether they have mixed anomalies with the gravitational background field (spacetime diffeomorphism under Spin group rotation) and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry protection with the fermion parity $\mathbb{Z}_2^{\rm F}$. While many Grand Unified Theories violating the discrete $\bf B + L$ symmetry suffer from the proton decay, the SM and some versions of Ultra Unification can have a stable proton., Comment: 5.5 pages. Sequel to arXiv:2112.14765

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions., Comment: 5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions., Comment: 5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG., Comment: 33 pages. An invited overview of Symmetric Mass Generation. Introduce a novel unifying theoretical framework. We thank Cenke Xu for initiating this project

For the 4d Standard Model (SM) with Lie group $G_{{\rm SM}_q} \equiv$ SU(3)$\times$SU(2)$\times$U(1)$_{\tilde Y}/\mathbb{Z}_q$ of $q=1,2,3,6$ with $N_f$ family of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamically gauged $G_{{\rm SM}_q}$, it is important to check whether they have mixed anomalies with the gravitational background field (spacetime diffeomorphism under Spin group rotation) and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry protection with the fermion parity $\mathbb{Z}_2^{\rm F}$. While many Grand Unified Theories violating the discrete $\bf B + L$ symmetry suffer from the proton decay, the SM and some versions of Ultra Unification can have a stable proton., Comment: 5.5 pages. Sequel to arXiv:2112.14765

This article overviews the recent developments in applying the idea of deconfined quantum criticality in condensed matter physics to understand quantum phase transitions among grand unified theories in high energy physics in the 4-dimensional spacetime. In particular, dictated by a mod 2 class nonperturbative global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models -- not only the Standard Model occurs as a neighbor phase, but also beyond the Standard Model phenomena (such as deconfined dark gauge force and fractionalized/fragmentary fermionic partons) emerge near the critical region., Comment: 9 pages. An overview on arXiv:2106.16248. An invited contribution to Professor Chen-Ning Yang Centenary 100 anniversary Festschrift

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions., Comment: 5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG., Comment: 33 pages. An invited overview of Symmetric Mass Generation. Introduce a novel unifying theoretical framework. We thank Cenke Xu for initiating this project

For the 4d Standard Model (SM) with Lie group $G_{{\rm SM}_q} \equiv$ SU(3)$\times$SU(2)$\times$U(1)$_{\tilde Y}/\mathbb{Z}_q$ of $q=1,2,3,6$ with $N_f$ family of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamically gauged $G_{{\rm SM}_q}$, it is important to check whether they have mixed anomalies with the gravitational background field (spacetime diffeomorphism under Spin group rotation) and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry protection with the fermion parity $\mathbb{Z}_2^{\rm F}$. While many Grand Unified Theories violating the discrete $\bf B + L$ symmetry suffer from the proton decay, the SM and some versions of Ultra Unification can have a stable proton., Comment: 5.5 pages. Sequel to arXiv:2112.14765

This article overviews the recent developments in applying the idea of deconfined quantum criticality in condensed matter physics to understand quantum phase transitions among grand unified theories in high energy physics in the 4-dimensional spacetime. In particular, dictated by a mod 2 class nonperturbative global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models -- not only the Standard Model occurs as a neighbor phase, but also beyond the Standard Model phenomena (such as deconfined dark gauge force and fractionalized/fragmentary fermionic partons) emerge near the critical region., Comment: 9 pages. An overview on arXiv:2106.16248. An invited contribution to Professor Chen-Ning Yang Centenary 100 anniversary Festschrift

We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\bar\theta_3 \simeq 0$ for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$ and without any quadratic mean-field mass deformation as long as $G$ is all perturbative local and nonperturbative global anomaly-free. In our first model, we propose a disordered non-mean-field SMG gap (instead of the ordered Anderson-Higgs induced mass gap) for the $u$ quark (or generally a set of quarks and leptons totally anomaly-free in $G$) generated by multi-fermion interactions or by dynamical disordered mass fields, absorbing $\bar\theta_3$. Another variant of this first model is the SMG gapping a hypothetical hidden full fourth family of SM fermions. In our second model, we have a chiral SM and mirror SM together to respect the Nielsen-Ninomiya fermion-doubling and a parity-reflection $\mathbb{Z}_2^{\rm PR}$ symmetry at high energy, so the $\bar\theta_3 = 0$. Then the SMG lifts only the mirror SM with a large energy gap but leaves the chiral SM at lower energy, which not only "spontaneously" breaks the parity-reflection symmetry maximally but also relates our solution to solve another nonperturbative chiral fermion regularization problem by removing the fermion doubling. The predictive signature of both SMG-based models is that some SM fermions or mirror fermions are highly interacting (beyond the conventional SM Higgs or SM gauge interactions) mediated through hypothetical direct multi-fermion or disordered mass-field interactions., Comment: 30 pages. A companion to arXiv:2207.14813. An overview on Symmetric Mass Generation arXiv:2204.14271

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction., Comment: 16 pages, 6 figures

We present a model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement (namely confinement without chiral symmetry breaking in a supersymmetric gauge theory) at an intermediate energy scale, before the electroweak symmetry breaking by the Higgs condensation at lower energy. In our context, the smooth confinement preserves the SU(3) and the chiral SU(2)$_L\times$ U(1)$_Y$ symmetry in a supersymmetric Standard Model, while this internal symmetry becomes dynamically gauged in the end. In contrast to Razamat-Tong's symmetric mass generation model also preserving the $G_{\rm SM} \equiv$ SU(3)$_C\times$ SU(2)$_L\times$ U(1)$_Y$ internal symmetry, our model introduces different matter contents with a different kind of superpotential deformation irrelevant at UV, which further induces Yukawa-Higgs terms marginal at IR, breaking the $G_{\rm SM}$ down to SU(3)$_C$ and the electromagnetic U(1)$_{\rm EM}$ only when Higgs condenses. In our model, the IR fermions in the first and second families are composite of UV fields, while the third family elementary fermions match between UV and IR. The smallness of the first and second family fermion masses is explained by the exponential hierarchy between the cutoff scale and the smooth confinement scale via dimensional transmutation. As a result, our UV Lagrangian only contains the natural parameters close to the order one., Comment: 11 pages, 1 figure (v1); references add, modifications for clarity (v2); matches published version (v3)

An analogous "Strong CP problem" is identified in a toy model in 2-dimensional spacetime: a general 1+1d abelian U(1) anomaly-free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\theta}{2 \pi} \int F$. The theta term alone violates the charge-conjugation-time-reversal CT and the parity P discrete symmetries. The analogous puzzle here is the CT or P problem in 1+1d: Why can the $\bar{\theta}$ angle (including the effect of $\theta$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this CT or P problem can be solved by a Symmetric Mass Generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly-free symmetry). This 1+1d toy model mimics several features of the 3+1d Standard Model: chiral matter content, confinement, and Anderson-Higgs-induced mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection PR discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly-free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest 1+1d U(1) symmetric anomaly-free chiral fermion/gauge theory (e.g., Weyl fermions with $3_L$-$4_L$-$5_R$-$0_R$ U(1) charges) is demonstrated. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the Peccei-Quinn solution sitting in the (quasi-long-range-order) superfluid phase, our solution is in the SMG insulator disordered phase., Comment: 28 pages. Two classes of solutions, without or with the mirror fermion sector. A companion to arXiv:2212.14036. Related models: arXiv:1307.7480, arXiv:1807.05998, arXiv:2202.12355. v3: More misprints corrected. New refinement and clarification upon the Physical Review D version

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG., Comment: 33 pages. An invited overview of Symmetric Mass Generation. Introduce a novel unifying theoretical framework. We thank Cenke Xu for initiating this project

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction., Comment: 16 pages, 6 figures

We present a model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement (namely confinement without chiral symmetry breaking in a supersymmetric gauge theory) at an intermediate energy scale, before the electroweak symmetry breaking by the Higgs condensation at lower energy. In our context, the smooth confinement preserves the SU(3) and the chiral SU(2)$_L\times$ U(1)$_Y$ symmetry in a supersymmetric Standard Model, while this internal symmetry becomes dynamically gauged in the end. In contrast to Razamat-Tong's symmetric mass generation model also preserving the $G_{\rm SM} \equiv$ SU(3)$_C\times$ SU(2)$_L\times$ U(1)$_Y$ internal symmetry, our model introduces different matter contents with a different kind of superpotential deformation irrelevant at UV, which further induces Yukawa-Higgs terms marginal at IR, breaking the $G_{\rm SM}$ down to SU(3)$_C$ and the electromagnetic U(1)$_{\rm EM}$ only when Higgs condenses. In our model, the IR fermions in the first and second families are composite of UV fields, while the third family elementary fermions match between UV and IR. The smallness of the first and second family fermion masses is explained by the exponential hierarchy between the cutoff scale and the smooth confinement scale via dimensional transmutation. As a result, our UV Lagrangian only contains the natural parameters close to the order one., Comment: 11 pages, 1 figure; references add, modifications for clarity (v2)

An analogous "Strong CP problem" is identified in a toy model in 2-dimensional spacetime: a general 1+1d abelian U(1) anomaly-free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\theta}{2 \pi} \int F$. The theta term alone violates the charge-conjugation-time-reversal CT and the parity P discrete symmetries. The analogous puzzle here is the CT or P problem in 1+1d: Why can the $\bar{\theta}$ angle (including the effect of $\theta$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this CT or P problem can be solved by a Symmetric Mass Generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly-free symmetry). This 1+1d toy model mimics several features of the 3+1d Standard Model: chiral matter content, confinement, and Anderson-Higgs-induced mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection PR discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly-free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest 1+1d U(1) symmetric anomaly-free chiral fermion/gauge theory (e.g., Weyl fermions with $3_L$-$4_L$-$5_R$-$0_R$ U(1) charges) is demonstrated. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the Peccei-Quinn solution sitting in the (quasi-long-range-order) superfluid phase, our solution is in the SMG insulator disordered phase., Comment: 28 pages. Two classes of solutions, without or with the mirror fermion sector. A companion to arXiv:2212.14036. Related models: arXiv:1307.7480, arXiv:1807.05998, arXiv:2202.12355. v3: More misprints corrected. New refinement and clarification upon the Physical Review D version

We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\bar\theta_3 \simeq 0$ for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$ and without any quadratic mean-field mass deformation as long as $G$ is all perturbative local and nonperturbative global anomaly-free. In our first model, we propose a disordered non-mean-field SMG gap (instead of the ordered Anderson-Higgs induced mass gap) for the $u$ quark (or generally a set of quarks and leptons totally anomaly-free in $G$) generated by multi-fermion interactions or by dynamical disordered mass fields, absorbing $\bar\theta_3$. Another variant of this first model is the SMG gapping a hypothetical hidden full fourth family of SM fermions. In our second model, we have a chiral SM and mirror SM together to respect the Nielsen-Ninomiya fermion-doubling and a parity-reflection $\mathbb{Z}_2^{\rm PR}$ symmetry at high energy, so the $\bar\theta_3 = 0$. Then the SMG lifts only the mirror SM with a large energy gap but leaves the chiral SM at lower energy, which not only "spontaneously" breaks the parity-reflection symmetry maximally but also relates our solution to solve another nonperturbative chiral fermion regularization problem by removing the fermion doubling. The predictive signature of both SMG-based models is that some SM fermions or mirror fermions are highly interacting (beyond the conventional SM Higgs or SM gauge interactions) mediated through hypothetical direct multi-fermion or disordered mass-field interactions., Comment: 30 pages. A companion to arXiv:2207.14813. An overview on Symmetric Mass Generation arXiv:2204.14271

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction., Comment: 16 pages, 6 figures

We present a model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement (namely confinement without chiral symmetry breaking in a supersymmetric gauge theory) at an intermediate energy scale, before the electroweak symmetry breaking by the Higgs condensation at lower energy. In our context, the smooth confinement preserves the SU(3) and the chiral SU(2)$_L\times$ U(1)$_Y$ symmetry in a supersymmetric Standard Model, while this internal symmetry becomes dynamically gauged in the end. In contrast to Razamat-Tong's symmetric mass generation model also preserving the $G_{\rm SM} \equiv$ SU(3)$_C\times$ SU(2)$_L\times$ U(1)$_Y$ internal symmetry, our model introduces different matter contents with a different kind of superpotential deformation irrelevant at UV, which further induces Yukawa-Higgs terms marginal at IR, breaking the $G_{\rm SM}$ down to SU(3)$_C$ and the electromagnetic U(1)$_{\rm EM}$ only when Higgs condenses. In our model, the IR fermions in the first and second families are composite of UV fields, while the third family elementary fermions match between UV and IR. The smallness of the first and second family fermion masses is explained by the exponential hierarchy between the cutoff scale and the smooth confinement scale via dimensional transmutation. As a result, our UV Lagrangian only contains the natural parameters close to the order one., Comment: 11 pages, 1 figure (v1); references add, modifications for clarity (v2); matches published version (v3)

An analogous "Strong CP problem" is identified in a toy model in 2-dimensional spacetime: a general 1+1d abelian U(1) anomaly-free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\theta}{2 \pi} \int F$. The theta term alone violates the charge-conjugation-time-reversal CT and the parity P discrete symmetries. The analogous puzzle here is the CT or P problem in 1+1d: Why can the $\bar{\theta}$ angle (including the effect of $\theta$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this CT or P problem can be solved by a Symmetric Mass Generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly-free symmetry). This 1+1d toy model mimics several features of the 3+1d Standard Model: chiral matter content, confinement, and Anderson-Higgs-induced mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection PR discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly-free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest 1+1d U(1) symmetric anomaly-free chiral fermion/gauge theory (e.g., Weyl fermions with $3_L$-$4_L$-$5_R$-$0_R$ U(1) charges) is demonstrated. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the Peccei-Quinn solution sitting in the (quasi-long-range-order) superfluid phase, our solution is in the SMG insulator disordered phase., Comment: 28 pages. Two classes of solutions, without or with the mirror fermion sector. A companion to arXiv:2212.14036. Related models: arXiv:1307.7480, arXiv:1807.05998, arXiv:2202.12355. v3: More misprints corrected. New refinement and clarification upon the Physical Review D version

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions., Comment: 5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamical SM gauge field, it is important to check whether they have mixed anomalies with the gravitational background field and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of discrete ${\bf B + L}$ symmetry protection, in particular (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry with the fermion parity $\mathbb{Z}_2^{\rm F}$., Comment: 6 pages. Sequel to arXiv:2112.14765. v2: refinement. Related talks: https://www.youtube.com/results?search_query=cobordism+deformation+standard+model+crticiality. The original title "Proton Stability: From the Standard Model to Ultra Unification" is adjusted in PRD

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG., Comment: 33 pages. An invited overview of Symmetric Mass Generation. Introduce a novel unifying theoretical framework. We thank Cenke Xu for initiating this project

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction., Comment: 16 pages, 6 figures

We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\bar\theta_3 \simeq 0$ for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$ and without any quadratic mean-field mass deformation as long as $G$ is all perturbative local and nonperturbative global anomaly-free. In our first model, we propose a disordered non-mean-field SMG gap (instead of the ordered Anderson-Higgs induced mass gap) for the $u$ quark (or generally a set of quarks and leptons totally anomaly-free in $G$) generated by multi-fermion interactions or by dynamical disordered mass fields, absorbing $\bar\theta_3$. Another variant of this first model is the SMG gapping a hypothetical hidden full fourth family of SM fermions. In our second model, we have a chiral SM and mirror SM together to respect the Nielsen-Ninomiya fermion-doubling and a parity-reflection $\mathbb{Z}_2^{\rm PR}$ symmetry at high energy, so the $\bar\theta_3 = 0$. Then the SMG lifts only the mirror SM with a large energy gap but leaves the chiral SM at lower energy, which not only "spontaneously" breaks the parity-reflection symmetry maximally but also relates our solution to solve another nonperturbative chiral fermion regularization problem by removing the fermion doubling. The predictive signature of both SMG-based models is that some SM fermions or mirror fermions are highly interacting (beyond the conventional SM Higgs or SM gauge interactions) mediated through hypothetical direct multi-fermion or disordered mass-field interactions., Comment: 30 pages. A companion to arXiv:2207.14813. An overview on Symmetric Mass Generation arXiv:2204.14271