193 results on '"SU(2)"'
Search Results
2. Quantum field theory for coherent photons: isomorphism between Stokes parameters and spin expectation values.
- Author
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Saito, Shinichi, Li, Kangkang, and Shen, Yijie
- Subjects
QUANTUM field theory ,STOKES parameters ,ISOMORPHISM (Mathematics) ,PHOTONS ,COHERENCE (Physics) - Abstract
This article explores the use of Sn nanoparticles to enhance the optical properties of PEDOT: PSS thin films. The study focuses on the impact of Sn concentration on the films' optical characteristics, particularly in relation to organic solar cells. The results indicate that incorporating Sn nanoparticles improves the energy bandgap values and decreases the dielectric constant of the films, resulting in improved transmittance velocity and increased efficacy of microelectronic devices. The findings suggest that Sn-incorporated PEDOT: PSS thin films have potential applications in the field of optoelectronics and microelectronics. [Extracted from the article]
- Published
- 2024
- Full Text
- View/download PDF
3. Quantum field theory for coherent photons: isomorphism between stokes parameters and spin expectation values.
- Author
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Shinichi Saito, Kangkang Li, and Yijie Shen
- Subjects
QUANTUM field theory ,STOKES parameters ,PHOTONS ,COHERENT states ,GROUP theory ,POLARIZATION (Nuclear physics) - Abstract
Stokes parameters (S) on the Poincaré sphere are very useful values to describe the polarisation state of photons. However, the fundamental principle on the nature of polarisation is not completely understood, yet, because we have no concrete consensus on how to describe spin of photons, quantum-mechanically. Here, we have considered a monochromatic coherent ray of photons, described by a many-body coherent state, and established a fundamental basis to describe the spin state of photons, in connection with a classical description based on Stokes parameters. We show that a spinor description of the coherent state is equivalent to Jones vector for polarisation states, and obtain the spin operators (Ŝ) of all components based on rotators in an SU(2) group theory. Polarisation controllers such as phase-shifters and rotators are also obtained as quantummechanical field operators to change the phase of the wavefunction for polarisation states. We show that the Stokes parameters are quantummechanical average of the spin operators, S = ⟨Ŝ⟩. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Yang–Mills field strength and classical trajectories of electrons in Rashba spin–orbit-coupled systems
- Author
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Hong, Jinki, Kim, Hyoungtae, and Kim, Sangsu
- Published
- 2024
- Full Text
- View/download PDF
5. Active SU(2) operation on Poincaré sphere
- Author
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Shinichi Saito
- Subjects
Coherent state ,Lie algebra ,Spin angular momentum ,SU(2) ,Polarisation ,Poincaré sphere ,Physics ,QC1-999 - Abstract
Polarisation is described by an SU(2) state due to the coherence of photons emitted from a ubiquitous laser source. We propose a polarisation modulator, called as a Poincaré rotator, which enables dynamic control over a polarisation state by executing an arbitrary rotation on the Poincaré sphere. The Poincaré rotator works as an arbitrary operator in the SU(2) Lie group, combining two U(1) operations to change the phase and the amplitude of the state, respectively. By modulating both the phase and amplitude, we have achieved distinguishable 4×4=16, 8×8=64, and 10×10=100 states on the Poincaré sphere. As a locus of the polarisation states on the sphere, we have successfully drawn the molecular structure of Buckminsterfullerene (C60) and the coastline of the Earth.
- Published
- 2024
- Full Text
- View/download PDF
6. Special theory of relativity for a graded index fibre
- Author
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Shinichi Saito
- Subjects
Stokes parameters ,Poincaré sphere ,polarisation ,spin angular momentum ,SU(2) ,coherent state ,Physics ,QC1-999 - Abstract
The speed of light (c) in a vacuum is independent of the choice of frames to describe the propagation, according to the theory of relativity. We consider how light is characterised in a material, where the speed of light is different from that in a vacuum due to the finite dielectric constant. The phase velocity in a material is smaller than c, such that the speed of a moving frame can be larger than the phase velocity, such that the frame can move faster than the speed of light in a material. Consequently, an unusual Doppler effect is expected, and the wavelength in the moving frame changes from the red-shift to the blue-shift upon increasing the speed of the frame. The corresponding energy of the light also changes sign from positive to negative, while momentum is always positive, leading to the changes of signs for the phase velocity and the helicity. In a graded index fibre, where the exact solution is available, even more complicated phenomena are expected, due to the finite effective mass of photons. Upon the increase of the energy gap, generated by optical confinements and optical orbital angular momentum, the effective mass of photons increases. If the gap is large enough, momentum starts to change the sign upon increasing the frame velocity, while the energy of photons is always positive. In this case, the phase velocity diverges if momentum is in agreement with the fame velocity. Contrary to the unusual behaviours of the phase velocity, the group velocity is always below c. This thought experiment might be useful for considering insight into the polarisation state of light.
- Published
- 2023
- Full Text
- View/download PDF
7. Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space ℝp,q.
- Author
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Shirokov, Dmitry
- Subjects
- *
SINGULAR value decomposition , *ABELIAN functions , *CUBIC equations , *GAUGE symmetries , *PERTURBATION theory , *EQUATIONS - Abstract
We present a classification and an explicit form of all constant solutions of the Yang–Mills equations with SU (2) gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ℝ p , q of arbitrary finite dimension n = p + q. Using hyperbolic singular value decomposition and two-sheeted covering of orthogonal group by spin group, we solve the nontrivial system for constant solutions of the Yang–Mills equations of 3 n cubic equations with 3 n unknowns and 3 n parameters in the general case. We present a new symmetry of this system of equations. All solutions in terms of the potential, strength and invariant of the Yang–Mills field are presented. Nonconstant solutions of the Yang–Mills equations can be considered in the form of series of perturbation theory using all constant solutions as a zeroth approximation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
8. SU(2) symmetry of coherent photons and application to Poincaré rotator
- Author
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Shinichi Saito
- Subjects
Stokes parameters ,Poincaré sphere ,polarisation ,spin angular momentum ,SU(2) ,coherent state ,Physics ,QC1-999 - Abstract
Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider SU(2) wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship to spin expectation values with SO(3) symmetry based on isomorphism theorems. In particular, we found rotated half-wave-plates correspond to mirror reflections in the Poincaré sphere, which do not form a subgroup in the projected O(2) plane due to anti-hermitian property. This could be overcome experimentally by preparing another half-wave-plate to realise a pristine rotator in SU(2), which allows arbitrary rotation angles determined by the physical rotation. By combining another 2 quarter-wave-plates, we could also construct a genuine phase-shifter, thus, realising passive control over the full Poincaré sphere.
- Published
- 2023
- Full Text
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9. On the Dirac Spectrum of Homogeneous 3-Spheres.
- Author
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Kling, Jordi and Schueth, Dorothee
- Abstract
We show that any two left-invariant metrics on S 3 ≅ SU (2) which are isospectral for the associated classical Dirac operator D must be isometric. In the case of left-invariant metrics of positive scalar curvature, we compute and use the smallest eigenvalue of D 2 . We show analogous results for left-invariant metrics on SO (3) = S 3 / { ± 1 } for each of its two spin structures. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
10. Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations.
- Author
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Shirokov, D. S.
- Subjects
- *
SINGULAR value decomposition , *GAUGE symmetries , *PERTURBATION theory , *EQUATIONS , *LIE groups - Abstract
The hyperbolic singular value decomposition is used for studying the Yang–Mills equations with SU(2) gauge symmetry and the Yang–Mills–Proca equations in a pseudo-Euclidean (or Euclidean) space of an arbitrary finite dimension and signature. An explicit form of all constant solutions to the system of Yang–Mills–Proca equations in the case of the Lie group SU(2) is obtained. Nonconstant solutions to the Yang–Mills–Proca equations are considered as perturbation theory series. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
11. Multiple Multi-Orbit Pairing Algebras in Nuclei
- Author
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Venkata Krishna Brahmam Kota and Rankanidhi Sahu
- Subjects
pairing ,multiple algebras ,multi-j shell model ,interacting boson models ,SU(2) ,SO(5) ,Mathematics ,QA1-939 - Abstract
The algebraic group theory approach to pairing in nuclei is an old subject and yet it continues to be important in nuclear structure, giving new results. It is well known that for identical nucleons in the shell model approach with j − j coupling, pairing algebra is SU(2) with a complementary number-conserving Sp(N) algebra and for nucleons with good isospin, it is SO(5) with a complementary number-conserving Sp(2Ω) algebra. Similarly, with L − S coupling and isospin, the pairing algebra is SO(8). On the other hand, in the interacting boson models of nuclei, with identical bosons (IBM-1) the pairing algebra is SU(1, 1) with a complementary number-conserving SO(N) algebra and for the proton–neutron interacting boson model (IBM-2) with good F-spin, it is SO(3, 2) with a complementary number-conserving SO(ΩB) algebra. Furthermore, in IBM-3 and IBM-4 models several pairing algebras are possible. With more than one j or ℓ orbit in shell model, i.e., in the multi-orbit situation, the pairing algebras are not unique and we have the new paradigm of multiple pairing [SU(2), SO(5) and SO(8)] algebras in shell models and similarly there are multiple pairing algebras [SU(1, 1), SO(3, 2) etc.] in interacting boson models. A review of the results for multiple multi-orbit pairing algebras in shell models and interacting boson models is presented in this article with details given for multiple SU(2), SO(5), SU(1, 1) and SO(3, 2) pairing algebras. Some applications of these multiple pairing algebras are discussed. Finally, multiple SO(8) pairing algebras in shell model and pairing algebras in IBM-3 model are briefly discussed.
- Published
- 2023
- Full Text
- View/download PDF
12. Operators and Field Equations in the Electroweak Sector of Particle Physics.
- Author
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McClellan, Gene E.
- Abstract
This paper derives a linear, first-order, partial differential field equation (a Dirac-like equation) in the geometric calculus of the geometric algebra G 4 , 1 that has free plane-wave solutions distinct from one another that correspond to the left and right chiral states of the electron and the neutrino. Besides the usual spacetime dependence of plane waves, the solutions have a multivector structure yielding a ladder of states with raising and lowering operators appropriate to electroweak theory and having an S U (2) L relationship among the chiral electron and neutrino states. The required Dirac-like equation in G 4 , 1 results from a systematic review of Dirac-like equations (i.e., first-order field equations whose solutions also satisfy the Klein–Gordon equation) in geometric algebras of lower dimension. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
13. Active SU(2) operation on Poincaré sphere.
- Author
-
Saito, Shinichi
- Abstract
Polarisation is described by an SU(2) state due to the coherence of photons emitted from a ubiquitous laser source. We propose a polarisation modulator, called as a Poincaré rotator, which enables dynamic control over a polarisation state by executing an arbitrary rotation on the Poincaré sphere. The Poincaré rotator works as an arbitrary operator in the SU(2) Lie group, combining two U(1) operations to change the phase and the amplitude of the state, respectively. By modulating both the phase and amplitude, we have achieved distinguishable 4 × 4 = 16 , 8 × 8 = 64 , and 10 × 10 = 100 states on the Poincaré sphere. As a locus of the polarisation states on the sphere, we have successfully drawn the molecular structure of Buckminsterfullerene (C 60) and the coastline of the Earth. • A new device called Poincaré rotator is proposed to enable polarisation control. • An arbitrary SU(2) operation can be applied to coherent photons. • C 60 and the Earth were drawn on the Poincaré sphere. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Solid-state Stern–Gerlach spin splitter for magnetic field sensing, spintronics, and quantum computing
- Author
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Kristofer Björnson and Annica M. Black-Schaffer
- Subjects
Aharanov–Bohm ,quantum computing ,spintronics ,Stern–Gerlach ,SU(2) ,topological insulator ,Technology ,Chemical technology ,TP1-1185 ,Science ,Physics ,QC1-999 - Abstract
We show conceptually that the edge of a two-dimensional topological insulator can be used to construct a solid-state Stern–Gerlach spin splitter. By threading such a Stern–Gerlach apparatus with a magnetic flux, Aharanov–Bohm-like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit SU(2)-gate, one of the two gates required for a universal quantum computer. The field sensitivity, or switching field, b, is related to the characteristic size of the device, r, through b = h/(2πqr2), with q being the unit of electric charge.
- Published
- 2018
- Full Text
- View/download PDF
15. Charging Quantum Batteries with a General Harmonic Driving Field.
- Author
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Chen, Jie, Zhan, Liyao, Shao, Lei, Zhang, Xingyu, Zhang, Yuyu, and Wang, Xiaoguang
- Subjects
- *
HARMONIC drives , *QUANTUM efficiency , *ELECTRIC batteries - Abstract
A general harmonic driving field was considered for improving the charging efficiency of the quantum battery system. Charge saturation was used to describe the charging efficiency, where the charging mode is divided into saturated and unsaturated. The relationships between the time‐dependent charge saturation and parameters of the general driving field were evaluated both analytically and numerically. The Floquet theorem was used to express time‐dependent charge saturation with the quasienergy and Floquet states of the system. The analytical and numerical results were used to identify the best parameter values for optimizing the charging efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
16. Nonabelian Monopoles
- Author
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Auzzi, Roberto
- Subjects
Physics of elementary particles and fields ,gauge field theory ,SU(2) ,gauge field theory ,USp(N) ,gauge field theory ,SO(N) ,spontaneous symmetry breaking ,magnetic monopole ,BPS ,mass ,supersymmetry ,fermion ,flavor ,group theory ,representation - Abstract
We study topological as well as dynamical properties of BPS nonabelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type in $ G=SU(N)$, $USp(2N)$ and SO(N) gauge theories, spontaneously broken to nonabelian subgroups $H$. We find that monopoles transform under the group dual to $H$ in a tensor representation of rank determined by the corresponding element in $\pi_1(H)$. When the system is embedded in a $\cal N=2$ supersymmetric theory with an appropriate set of flavors with appropriate bare masses, the BPS monopoles constructed semiclassically persist in the full quantum theory. This result supports the identification of "dual quarks'' found at $r$-vacua of $\cal N=2$ theories with the nonabelian magnetic monopoles. We present several consistency checks of our monopole spectra.
- Published
- 2009
17. Grupos, QED y Transiciones Radiativas
- Author
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Redondo Herrero, Carlos, Muñoz Castañeda, José María, Universidad de Valladolid. Facultad de Ciencias, Redondo Herrero, Carlos, Muñoz Castañeda, José María, and Universidad de Valladolid. Facultad de Ciencias
- Abstract
En este trabajo, estudiamos la simetría de SU (3) en el espacio de sabor de las partículas fundamentales (bariones y mesones) mediante el camino óctuple, y calculamos sus estados utilizando el modelo quark, como los quarks son una representación fundamental de SU (3) de sabor. Y usando la simetría calculamos diferentes propiedades, como sus momentos magnéticos, sus masas y sus transiciones radiativas., In this work, we study the SU (3) symmetry in the flavor of the elementary particles (baryons and mesons) via the eightfoldway, and calculate their state using the quark model, as quarks are a fundamental representation of flavor SU (3). And using this symmetry we calculate different properties, such as their magnetic moment, their mass and the radiative transitions., Departamento de Física Teórica, Atómica y Óptica, Grado en Física
- Published
- 2023
18. On electroweak symmetry breaking in the littlest Higgs model
- Author
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Dobado González, Antonio, Tabares Cheluci, Lourdes, Peñaranda, Siannah, Dobado González, Antonio, Tabares Cheluci, Lourdes, and Peñaranda, Siannah
- Abstract
© EPJ, Springer Verlag, Societá Italiana di Fisica. This work is supported by DGICYT (Spain) under project number BPA2005-02327. The work ofS.P. has been partially supported by the European Union under contract No. MEIF-CT-2003-500030. L.T. would like to thank Javier Almeida Linares (UCM, Spain) and Javier Rodriguez Laguna (SISSA, Italy) for their valuable guidance to C++ programming., In SU(5)/SO(5) little Higgs models radiative corrections give rise to SU(2)(L)xU(1)(Y) symmetry breaking. In this work we start a program for a detailed determination of the relevant terms of the effective Higgs potential by computing the contribution of the t, b and T quarks at the one-loop level, as a starting point for a higher-loop computation. In spite of the fact that some two-loop level contributions are well known to be important, we use our preliminary one-loop result to illustrate that, by demanding the effective potential to reproduce exactly the standard model Higgs potential, and in particular the relation m(H)(2)=2 lambda v(2)=2 mu(2), it will be possible to set new constraints on the parameter space of the littlest Higgs model when the computation of all the relevant contributions to the effective Higgs potential is completed., DGICYT (Spain), European Union, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub
- Published
- 2023
19. Phase-difference operator
- Author
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Luis Aina, Alfredo, Sánchez Soto, Luis Lorenzo, Luis Aina, Alfredo, and Sánchez Soto, Luis Lorenzo
- Abstract
© 1993 The American Physical Society. The authors would like to thank Professor A. Galindo and Professor R. Tanas for a critical reading of the manuscript and useful comments. They are grateful as well to Professor J.F. Carinena for helpful and enlightening discussions of some rather technical points. Finally, they benefited from the continuous interest and advice of Professor E. Bernabeu., We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields., Depto. de Óptica, Fac. de Ciencias Físicas, TRUE, pub
- Published
- 2023
20. Symmetries of Hamiltonians describing systems with arbitrary spins.
- Author
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Cervia, Michael J., Patwardhan, Amol V., and Balantekin, A. B.
- Subjects
- *
SYMMETRY , *NEUTRINO oscillation , *SPIN-spin interactions , *POLYNOMIALS , *EQUATIONS - Abstract
We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial relationships between the operator invariants, or equivalently, between eigenvalues of those invariants. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down
- Author
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Gerrit Coddens
- Subjects
quantum mechanics ,SU(2) ,Stern–Gerlach experiment ,spinors ,Mathematics ,QA1-939 - Abstract
The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry. Contrary to what Pauli has been reading into the Stern–Gerlach experiment, the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured. Surprisingly, this leads to only two energy states, which should be qualified as precession-up and precession-down rather than spin-up and spin-down. Indeed, despite the presence of the many different possible angles θ between the spin axis s and the magnetic field B, the fermions can only have two possible energies m0c2±μB. The values ±μB thus do not correspond to the continuum of values −μ·B Einstein and Ehrenfest had conjectured. The energy term V=−μ·B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB are not potential-energy states. We also explain the mathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clear and understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.
- Published
- 2021
- Full Text
- View/download PDF
22. Integrated Correlators in $\mathcal{N}=4$ SYM via $SL(2,\mathbb{Z})$ Spectral Theory
- Author
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Paul, Hynek, Perlmutter, Eric, Raj, Himanshu, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and HEP, INSPIRE
- Subjects
High Energy Physics - Theory ,dimension: 4 ,semiclassical ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,coupling: gauge ,FOS: Physical sciences ,algebra ,localization ,multiplet: tensor ,conformal ,High Energy Physics - Theory (hep-th) ,space-time ,SU(2) ,tensor: energy-momentum ,gauge field theory: Yang-Mills ,anti-de Sitter ,spectral ,Toda ,[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th] ,supergravity ,n-point function: 4 ,correlation function ,supersymmetry ,SU(N) ,lattice - Abstract
We perform a systematic study of integrated four-point functions of half-BPS operators in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(N)$. These observables, defined by a certain spacetime integral of $\langle\mathcal{O}_2\mathcal{O}_2\mathcal{O}_p\mathcal{O}_p\rangle$ where $\mathcal{O}_p$ is a superconformal primary of charge $p$, are known to be computable by supersymmetric localization, yet are non-trivial functions of the complexified gauge coupling $\tau$. We find explicit and remarkably simple results for several classes of these observables, exactly as a function of $N$ and $\tau$. Their physical and formal properties are greatly illuminated upon employing the $SL(2,\mathbb{Z})$ spectral decomposition: in this S-duality-invariant eigenbasis, the integrated correlators are fixed simply by polynomials in the spectral parameter. These polynomials are determined recursively by linear algebraic equations relating different $N$ and $p$, such that all integrated correlators are ultimately fixed in terms of the integrated stress tensor multiplets in the $SU(2)$ theory. Our computations include the full matrix of integrated correlators at low values of $p$, and a certain infinite class involving operators of arbitrary $p$. The latter satisfy an open lattice chain equation for all $N$, reminiscent of the Toda equation obeyed by extremal correlators in $\mathcal{N}=2$ superconformal theories. We compute ensemble averages of these observables and analyze our solutions at large $N$, confirming and predicting features of semiclassical AdS$_5\, \times$ S$^5$ supergravity amplitudes., Comment: 42+24 pages
- Published
- 2023
23. Dark matter from the centre of SU(N)
- Author
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Frigerio, Michele, Grimbaum-Yamamoto, Nicolas, Hambye, Thomas, and HEP, INSPIRE
- Subjects
scalar ,photon ,FOS: Physical sciences ,spontaneous symmetry breaking ,stability ,field theory ,dark matter ,[PHYS.HPHE] Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,High Energy Physics - Phenomenology ,High Energy Physics - Phenomenology (hep-ph) ,annihilation ,SU(2) ,SU(3) ,gauge ,nonabelian ,coupling ,symmetry ,SU(N) - Abstract
A dark sector with non-abelian gauge symmetry provides a sound framework to justify stable dark matter (DM) candidates. We consider scalar fields charged under a $SU(N)$ gauge group, and show that the centre of $SU(N)$, the discrete subgroup $Z_N$ also known as $N$-ality, can ensure the stability of scalar DM particles. We analyse in some details two minimal DM models of this class, based on $SU(2)$ and $SU(3)$, respectively. These models have non-trivial patterns of spontaneous symmetry breaking, leading to distinctive phenomenological implications. For the $SU(2)$ model these include a specific interplay of two DM states, with the same interactions but different masses, and several complementary DM annihilation regimes, either within the dark sector or through the Higgs portal. The $SU(3)$ model predicts dark radiation made of a pair of dark photons with a unique gauge coupling, as well as regimes where DM semi-annihilations become dominant and testable., 27 pages, 5 figures
- Published
- 2023
24. 3D Quantum Gravity from Holomorphic Blocks
- Author
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Etera R. Livine, Qiaoyin Pan, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), and École normale supérieure de Lyon (ENS de Lyon)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)
- Subjects
High Energy Physics - Theory ,geometry ,dimension: 3 ,partition function ,pole ,FOS: Physical sciences ,General Relativity and Quantum Cosmology (gr-qc) ,holomorphic ,spin ,General Relativity and Quantum Cosmology ,quantum geometry ,Ising model ,continuum limit ,structure ,spinor ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Ponzano-Regge model ,critical phenomena ,field theory: topological ,buildings ,High Energy Physics - Theory (hep-th) ,space-time ,SU(2) ,gravitation ,twist ,[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,duality ,path integral - Abstract
Three-dimensional gravity is a topological field theory, which can be quantized as the Ponzano-Regge state-sum model built from the $\{3nj\}$-symbols of the recoupling of the $\SU(2)$ representations, in which spins are interpreted as quantized edge lengths in Planck units. It describes the flat spacetime as gluing of three-dimensional cells with a fixed boundary metric encoding length scale. In this paper, we revisit the Ponzano-Regge model formulated in terms of spinors and rewrite the quantum geometry of 3D cells with holomorphic recoupling symbols. These symbols, known as Schwinger's generating function for the $\{6j\}$-symbols, are simply the squared inverse of the partition function of the 2D Ising model living on the boundary of the 3D cells. They can furthermore be interpreted, in their critical regime, as scale-invariant basic elements of geometry. We show how to glue them together into a discrete topological quantum field theory. This reformulation of the path integral for 3D quantum gravity, with a rich pole structure of the elementary building blocks, opens a new door toward the study of phase transitions and continuum limits in 3D quantum gravity, and offers a new twist on the construction of a duality between 3D quantum gravity and a 2d conformal theory., 42 pages + appendices, 18 figures
- Published
- 2023
25. Geometrical Properties of the SU(2)U(1) Gauge
- Author
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Boudet, Roger and Boudet, Roger
- Published
- 2011
- Full Text
- View/download PDF
26. Scalable Spin Squeezing from Spontaneous Breaking of a Continuous Symmetry
- Author
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Tommaso Comparin, Fabio Mezzacapo, Martin Robert-de-Saint-Vincent, Tommaso Roscilde, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des Lasers (LPL), and Université Paris 13 (UP13)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
- Subjects
collective ,FOS: Physical sciences ,General Physics and Astronomy ,spin ,magnetization ,Condensed Matter - Strongly Correlated Electrons ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,thermodynamical ,[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] ,qubit ,Quantum Physics ,model ,Strongly Correlated Electrons (cond-mat.str-el) ,fluctuation ,scaling ,spontaneous symmetry breaking ,suppression ,U(1) ,Hamiltonian ,transverse ,linear ,SU(2) ,Quantum Gases (cond-mat.quant-gas) ,adiabatic ,many-body problem ,Quantum Physics (quant-ph) ,entanglement ,Condensed Matter - Quantum Gases - Abstract
Spontaneous symmetry breaking (SSB) is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the case of quantum spin models with continuous symmetry, we show that this adiabatic process is also accompanied by the suppression of the fluctuations of the symmetry generator -- namely, the collective spin component along an axis of symmetry. In systems of $S=1/2$ spins or qubits, the combination of the suppression of fluctuations along one direction and of the persistence of transverse magnetization leads to spin squeezing -- a much sought-after property of quantum states, both for the purpose of entanglement detection as well as for metrological uses. Focusing on the case of XXZ models spontaneously breaking a U(1) (or even SU(2)) symmetry, we show that the adiabatically prepared states have nearly minimal spin uncertainty; that the minimum phase uncertainty that one can achieve with these states scales as $N^{-3/4}$ with the number of spins $N$; and that this scaling is attained after an adiabatic preparation time scaling linearly with $N$. Our findings open the door to the adiabatic preparation of strongly spin-squeezed states in a large variety of quantum many-body devices including e.g. optical lattice clocks., 5+3 pages, 3+6 figures
- Published
- 2022
27. Longitudinal mapping knot invariant for SU(2).
- Author
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Clark, W. Edwin and Saito, Masahico
- Subjects
- *
KNOT theory , *CARTOGRAPHY , *INVARIANTS (Mathematics) , *GENERALIZATION , *POLYNOMIALS - Abstract
The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn, this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group, then this invariant can be thought of as a topological generalization of the 2-cocycle invariant. The longitudinal mapping invariant is based on a meridian–longitude pair in the knot group. We also give an interpretation of the invariant in terms of quandle colorings of a 1-tangle for generalized Alexander quandles without use of a meridian–longitude pair in the knot group. The invariant values are concretely evaluated for the torus knots T (2 , n) , their mirror images, and the figure eight knot for the group SU(2). [ABSTRACT FROM AUTHOR]
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- 2018
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28. Lipschitz functions on SU(2) have uniformly convergent Fourier series.
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Myers, Donnie and Grow, David
- Subjects
- *
UNITARY groups , *FOURIER series , *LIPSCHITZ spaces , *LIE groups , *APPROXIMATION theory - Abstract
We demonstrate that the Fourier partial sums of a Lipschitz continuous function on the two-dimensional special unitary group converge uniformly to the function. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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29. On Pseudo-Differential Operators on Group SU(2)
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Ruzhansky, Michael, Turunen, Ville, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Bart, H., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Curto, R., editor, Davidson, K. R., editor, Demuth, M., editor, Dijksma, A., editor, Douglas, R. G., editor, Duduchava, R., editor, dos Santos, A. Ferreira, editor, Frazho, A. E., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevski, V., editor, Putinar, M., editor, Ran, A. C. M., editor, Rodman, L., editor, Rovnyak, J., editor, Schulze, B. -W., editor, Speck, F., editor, Spitkovsky, I. M., editor, Treil, S., editor, Tretter, C., editor, Upmeier, H., editor, Vasilevski, N., editor, Lunel, S. Verduyn, editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Rodino, Luigi, editor, and Wong, M. W., editor
- Published
- 2009
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30. Quantum Information: A Brief Overview and Some Mathematical Aspects
- Author
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Maurice R. Kibler
- Subjects
linearity ,superposition ,entanglement ,mutually unbiased bases ,SU(2) ,Galois fields ,Galois rings ,Mathematics ,QA1-939 - Abstract
The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.
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- 2018
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31. Introduction
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Boudet, Roger and Boudet, Roger
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- 2011
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32. On the traceless SU(2) character variety of the 6-punctured 2-sphere.
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Kirk, Paul
- Subjects
- *
KUMMER surfaces , *MATHEMATICAL mappings , *MATHEMATICAL singularities , *MATHEMATICAL proofs , *MATHEMATICAL analysis - Abstract
We exhibit the traceless SU(2) character variety of a 6-punctured 2-sphere as a 2-fold branched cover of , branched over the singular Kummer surface, with the branch locus in corresponding to the binary dihedral representations. This follows from an analysis of the map induced on SU(2) character varieties by the 2-fold branched cover branched over points, combined with the theorem of Narasimhan-Ramanan which identifies with . The singular points of correspond to abelian representations, and we prove that each has a neighborhood in homeomorphic to a cone on . [ABSTRACT FROM AUTHOR]
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- 2017
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33. Instanton gas approach to the Hubbard model
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Ulybyshev, Maksim, Winterowd, Christopher, Assaad, Fakher, Zafeiropoulos, Savvas, Centre de Physique Théorique - UMR 7332 (CPT), and Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
High Energy Physics - Theory ,Hubbard model ,geometry ,magnetic ,partition function ,FOS: Physical sciences ,spin ,decoupling ,Condensed Matter - Strongly Correlated Electrons ,High Energy Physics - Lattice ,Lefschetz thimbles ,gas ,mean field approximation ,thermodynamical ,structure ,[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat] ,capture ,symmetry ,lattice ,density ,Strongly Correlated Electrons (cond-mat.str-el) ,fluctuation ,[PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat] ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,formation ,High Energy Physics - Lattice (hep-lat) ,coupling constant ,transition ,saddle-point approximation ,71.10.Fd ,moment ,02.70.Ss ,SU(2) ,High Energy Physics - Theory (hep-th) ,correlation ,instanton ,11.15.Ha ,instantons ,spectral representation ,path integral - Abstract
In this article we consider a path integral formulation of the Hubbard model based on a SU(2)-symmetrical Hubbard-Stratonovich transformation that couples auxiliary field to the local electronic density. This decoupling is known to have a regular saddle-point structure: each saddle point is a set of elementary field configurations localized in space and imaginary time which we coin instantons. We formulate a classical partition function for the instanton gas that has predictive power. Namely, we can predict the distribution of instantons and show that the instanton number is sharply defined in the thermodynamic limit, thus defining a unique dominant saddle point. Despite the fact that the instanton approach does not capture the magnetic transition inherent to the Hubbard model on the honeycomb lattice, we were able to describe the local moment formation accompanied by short-ranged anti-ferromagnetic correlations. This aspect is also seen in the single particle spectral function that shows clear signs of the upper and lower Hubbard bands. Our instanton approach bears remarkable similarities to local dynamical approaches, such as dynamical mean field theory, in the sense that it has the unique property of allowing for local moment formation without breaking the SU(2) spin symmetry. In contrast to local approaches, it captures short-ranged magnetic fluctuations. Furthermore, it also offers possibilities for systematic improvements by taking into account fluctuations around the dominant saddle point. Finally, we show that the saddle point structure depends upon the choice of lattice geometry. For the square lattice at half-filling, the saddle point structure reflects the itinerant to localized nature of the magnetism as a function of the coupling strength. The implications of our results for Lefschetz thimbles approaches to alleviate the sign problem are also discussed., Comment: 32 pages, 29 figures
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- 2022
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34. The axion flavour connection
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Luc Darmé, Enrico Nardi, Clemente Smarra, and HEP, INSPIRE
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Nuclear and High Energy Physics ,flavor ,strong interaction ,anomaly ,spontaneous symmetry breaking ,FOS: Physical sciences ,hierarchy ,U(1) ,quark ,[PHYS.HPHE] Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,High Energy Physics - Phenomenology ,High Energy Physics - Phenomenology (hep-ph) ,CP ,dimension ,Peccei-Quinn ,SU(2) ,SU(3) ,quality ,axion ,quantum chromodynamics ,operator ,mass ,symmetry - Abstract
A local flavour symmetry acting on the quarks of the Standard Model can automatically give rise to an accidental global $U(1)$ which remains preserved from sources of explicit breaking up to a large operator dimension, while it gets spontaneously broken together with the flavour symmetry. Such non-fundamental symmetries are often endowed with a mixed QCD anomaly, so that the strong CP problem is automatically solved via the axion mechanism. We illustrate the general features required to realise this scenario, and we discuss a simple construction based on the flavour group $SU(3)\times SU(2) \times U(1)_F$ to illustrate how mass hierarchies can arise while ensuring at the same time a high quality Peccei-Quinn symmetry., Comment: 11 pages, no figures
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- 2022
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35. Asymptotics of $\mathrm {SL}(2,{{\mathbb {C}}})$ coherent invariant tensors
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Pierre Martin-Dussaud, Pietro Donà, Simone Speziale, Marco Fanizza, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), and Scuola Normale Superiore di Pisa (SNS)
- Subjects
High Energy Physics - Theory ,semiclassical ,Lorentz transformation ,EPRL model ,FOS: Physical sciences ,Semiclassical physics ,Spin foam ,General Relativity and Quantum Cosmology (gr-qc) ,Loop quantum gravity ,C) ,01 natural sciences ,General Relativity and Quantum Cosmology ,symbols.namesake ,representation: unitarity ,SL(2 ,0103 physical sciences ,asymptotic behavior ,Invariant (mathematics) ,010306 general physics ,transformation: Lorentz ,Mathematical Physics ,Special unitary group ,ComputingMilieux_MISCELLANEOUS ,Mathematical physics ,Physics ,Simplex ,010308 nuclear & particles physics ,higher-order: 0 ,deformation ,saddle-point approximation ,Statistical and Nonlinear Physics ,Clebsch–Gordan coefficients ,Mathematical Physics (math-ph) ,critical phenomena ,Clebsch-Gordan coefficients ,coherence ,High Energy Physics - Theory (hep-th) ,SU(2) ,gauge: time ,symbols ,[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,spin: foam ,field theory: vector ,simplex ,quantum gravity: loop space - Abstract
We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of $\mathrm{SL}(2,\mathbb{C})$ of the principal series, corresponding to generalized Clebsch-Gordan coefficients with $n\geq3$ legs. We find critical configurations of the quantum labels with a power-law decay of the invariants. They describe 3d polygons that can be deformed into one another via a Lorentz transformation. This is defined viewing the edge vectors of the polygons are the electric part of bivectors satisfying a (frame-dependent) relation between their electric and magnetic parts known as $\gamma$-simplicity in the loop quantum gravity literature. The frame depends on the SU(2) spin labelling the basis elements of the invariants. We compute a saddle point approximation using the critical points and provide a leading-order approximation of the invariants. The power-law is universal if the SU(2) spins have their lowest value, and $n$-dependent otherwise. As a side result, we provide a compact formula for $\gamma$-simplicity in arbitrary frames. The results have applications to the current EPRL model, but also to future research aiming at going beyond the use of fixed time gauge in spin foam models., Comment: 29 pages and 3 figures. v2:minor corrections and a subsection added to match published version
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- 2022
36. Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR
- Author
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Houri Ziaeepour, Univers, Transport, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213) (UTINAM), Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)
- Subjects
High Energy Physics - Theory ,cosmological model ,entanglement: quantum ,Physics and Astronomy (miscellaneous) ,dimension: 3 ,General Mathematics ,quantum cosmology ,FOS: Physical sciences ,quantum gravity: model ,General Relativity and Quantum Cosmology (gr-qc) ,algebra ,01 natural sciences ,Computer Science::Digital Libraries ,General Relativity and Quantum Cosmology ,group: representation ,0103 physical sciences ,Computer Science (miscellaneous) ,QA1-939 ,surface ,string model ,010306 general physics ,symmetry ,Quantum Physics ,010308 nuclear & particles physics ,quantum gravity ,background ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,Hilbert space ,16. Peace & justice ,High Energy Physics - Theory (hep-th) ,SU(2) ,Chemistry (miscellaneous) ,gravitation ,string ,[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,Computer Science::Programming Languages ,holography ,space-time: classical ,Quantum Physics (quant-ph) ,quantum gravity: loop space ,Mathematics - Abstract
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$ symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the $SU(\infty)$ representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space - the spacetime - has a 3+1 dimensional Lorentzian geometry. Here after a review of $SU(\infty)$-QGR, including the demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that such exercise gives a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: importance of 2D structures; algebraic decomposition to tensor products; special role of $SU(2)$ group in their formulation; necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in $SU(\infty)$-QGR without fine-tuning, additional assumptions, or restrictions., 39 pages, no figure
- Published
- 2022
37. Classical vs Quantum Eikonal Scattering and its Causal Structure
- Author
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Bellazzini, Brando, Isabella, Giulia, Riva, Massimiliano Maria, HEP, INSPIRE, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab), and Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
- Subjects
High Energy Physics - Theory ,eikonal ,higher-order ,spin ,rotation ,General Relativity and Quantum Cosmology ,correction: quantum ,High Energy Physics - Phenomenology (hep-ph) ,isometry ,quantum [correction] ,approximation ,scattering: eikonal ,fundamental constant: fine structure ,scattering [photon] ,[PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,classical [approximation] ,photon ,scattering: gravitation ,higher-order: 1 ,eikonal [scattering] ,interaction [gravitation] ,Effective Field Theories ,High Energy Physics - Phenomenology ,[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] ,gravitation: fundamental constant ,fine structure [fundamental constant] ,classical ,1 [higher-order] ,fundamental constant ,scalar ,Nuclear and High Energy Physics ,causality ,FOS: Physical sciences ,interaction ,General Relativity and Quantum Cosmology (gr-qc) ,field theory ,angular momentum ,quantum ,photon: scattering ,ddc:530 ,gravitation [scattering] ,structure ,scalar [field theory] ,Scattering Amplitudes ,fine structure ,fundamental constant [gravitation] ,gravitation: interaction ,scattering ,approximation: classical ,time delay ,field theory: scalar ,[PHYS.HPHE] Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,High Energy Physics - Theory (hep-th) ,SU(2) ,gravitation ,[PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,nonlinear ,[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th] ,correction - Abstract
Journal of high energy physics 04(4), 023 (2023). doi:10.1007/JHEP04(2023)023, We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the isometries of the plane, in the large angular momentum limit. We extend it to all orders in the scattering angle, and for all masses and spins. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We further investigate the competing classical vs quantum corrections to the leading classical eikonal scattering, and find several interesting examples where quantum corrections are more important than Post-Minkowskian's. As a case of study, we analyse the scattering of a photon off a massless neutral scalar field, up to next-to-leading order in the Newton constant, and to leading order in the fine structure constant. We investigate the causal structure of the eikonal regime and establish an infinite set of non-linear positivity bounds, of which positivity of time delay is the simplest., Published by SISSA, [Trieste]
- Published
- 2022
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- View/download PDF
38. Extending the Hong-Ou-Mandel effect: the power of nonclassicality
- Author
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Paul M. Alsing, Richard J. Birrittella, Christopher C. Gerry, Jihane Mimih, and Peter L. Knight
- Subjects
INTERFERENCE ,Quantum Physics ,Science & Technology ,PHOTON ,SU(2) ,Physics ,Physical Sciences ,FOS: Physical sciences ,Optics ,Physics, Atomic, Molecular & Chemical ,Quantum Physics (quant-ph) - Abstract
We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counter-intuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of non-classicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50/50 beam splitter is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50/50 BS can create total, or near total, destructive interference of quantum amplitudes. For odd photon number input Fock states of arbitrary value n>0 we show that the joint photon number probabilities vanish when detecting identical photon numbers in each output beams. We examine the mixing of photon number states of n = 1, 2, and 3 with a CV state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line -- a contiguous set of zeros representing complete destructive interference of quantum amplitudes. For odd or even photon number Fock states with n>1 there will be additional off-diagonal pseudo-nodal curves along which the joint photon number probabilities are either zero, or near zero, which constitute a near, but not complete, destructive interference., 27 pages, 13 figures; v2: minor editorial fixes (minor notational corrections in Appendix D), additional clarification comments at end of Appendix A
- Published
- 2021
39. Pants complex, TQFT and hyperbolic geometry
- Author
-
Detcherry, Renaud, Kalfagianni, Efstratia, HEP, INSPIRE, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB)
- Subjects
geometry ,asymptotic expansion ,graph theory ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,Geometric Topology (math.GT) ,[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph] ,field theory: topological ,Mathematics::Geometric Topology ,group: representation ,Mathematics - Geometric Topology ,SU(2) ,FOS: Mathematics ,surface ,space: noncompact - Abstract
We present a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, as developed by Blanchet, Habegger, Masbaum and Vogel, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this metric is quasi-isometric to the Teichm\"uller space with the Weil-Petersson metric and that the translation length of our metric provides two sided linear bounds on the volume of hyperbolic fibered manifolds. We also obtain a characterization of pseudo-Anosov mapping classes in terms of asymptotics of the quantum intersection number under iteration in the mapping class group and relate these asymptotics with stretch factors., Comment: 38 pages, 6 Figures. Minor changes in introduction, reference updated
- Published
- 2021
40. Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
- Author
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Dudal, David, van Egmond, Duifje Maria, Justo, Igor Figueiredo, Peruzzo, Giovani, Sorella, Silvio Paolo, Centre de Physique Théorique [Palaiseau] (CPHT), and Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
- Subjects
High Energy Physics - Theory ,operator: vector ,longitudinal ,High Energy Physics::Lattice ,FOS: Physical sciences ,renormalization: algebra ,Ward identity ,Higgs particle ,correction: quantum ,space-time: Euclidean ,symmetry: custodial ,invariance: gauge ,tree approximation ,correlation function ,perturbation theory ,Landau gauge ,vector boson ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,High Energy Physics::Phenomenology ,conservation law: Noether ,U(1) ,SU(2) ,High Energy Physics - Theory (hep-th) ,Higgs model ,quantization ,operator: composite - Abstract
The renormalization properties of two local gauge invariant composite operators $(O,R^a_{\mu})$ corresponding, respectively, to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are analyzed to all orders in perturbation theory by means of the algebraic renormalization in the $SU(2)$ Higgs model, with a single scalar in the fundamental representation, when quantized in the Landau gauge in Euclidean space-time. The present analysis generalizes earlier results presented in the case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an exact custodial symmetry, is derived for the first time, with deep consequences at the quantum level. In particular, the gauge invariant vector operators $R^a_{\mu}$ turn out to be the conserved Noether currents of the above-mentioned custodial symmetry. As such, these composite operators do not renormalize, as expressed by the fact that the renormalization $Z$-factors of the corresponding external sources, needed to define the operators $R^a_{\mu}$ at the quantum level, do not receive any quantum corrections. Another consistency feature of our analysis is that the longitudinal component of the two-point correlation function $\langle R^a_\mu(p) R^b_\nu(-p) \rangle$ exhibits only a tree level non-vanishing contribution which, moreover, is momentum independent, being thus not associated to any physical propagating mode. Finally, we point out that the renowned non-renormalization theorem for the ghost-antighost-vector boson vertex in Landau gauge remains true to all orders, also in presence of the Higgs field.
- Published
- 2021
41. Applying machine learning methods to prediction problems of lattice observables
- Author
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Gerasimeniuk, N. V., Chernodub, M. N., Goy, V. A., Boyda, D. L., Liubimov, S. D., Molochkov, A. V., Pacific Quantum Center [Vladivostok], Far Eastern Federal University (FEFU), Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Argonne National Laboratory [Lemont] (ANL), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO)
- Subjects
neural network ,[PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat] ,High Energy Physics::Lattice ,High Energy Physics - Lattice (hep-lat) ,FOS: Physical sciences ,critical phenomena ,High Energy Physics - Lattice ,SU(2) ,SU(3) ,correlation ,[PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,gauge ,invariance ,gauge field theory ,[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] ,lattice - Abstract
We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space., 7 pages, 2 figures, 1 table, contribution to the proceedings of XXXIII International (ONLINE) Workshop on High Energy Physics "Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests" November 8-12, 2021, Submission to SciPost
- Published
- 2021
42. Precision $B^*B\pi$ coupling from three-flavor lattice QCD
- Author
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Gérardin, Antoine, Heitger, Jochen, Kuberski, Simon, Simma, Hubert, Sommer, Rainer, ALPHA Collaboration, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), and ALPHA
- Subjects
flavor ,pi, mass ,[PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat] ,High Energy Physics::Lattice ,High Energy Physics::Phenomenology ,lattice field theory ,hep-lat ,perturbation theory: chiral ,Particle Physics - Lattice ,meson, chiral ,pi: mass ,perturbation theory, chiral ,meson: chiral ,quark ,High Energy Physics - Lattice ,meson, heavy ,SU(2) ,quantum chromodynamics ,meson: heavy ,flavor: 3 ,High Energy Physics::Experiment ,Nuclear Experiment ,lattice - Abstract
We consider three-flavor QCD and perform a determination of the low-energy coupling $\hat{g}_\chi$ of SU(2) Heavy Meson Chiral Perturbation Theory. It is the $B^*B\pi$ coupling in the limit of static heavy and chiral light quarks and has not been determined with precision thus far. The calculation is performed on a large set of the $2+1$ flavor CLS ensembles with pion masses from 420 MeV down to 130 MeV. This allows us to significantly reduce the systematic uncertainty from the chiral extrapolation compared to previous works. Only a weak dependence on the lattice spacing is visible in our results., Comment: 9 pages, 4 figures, The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021, Zoom/Gather@Massachusetts Institute of Technology
- Published
- 2021
- Full Text
- View/download PDF
43. SU(2) hyper-clocks with optimal quantum control of composite phase-shifts
- Author
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Zanon-Willette, Thomas, Laboratoire d'Etude du Rayonnement et de la Matière en Astrophysique (LERMA (UMR_8112)), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
- Subjects
engineering ,interferometer ,interference ,oscillation ,sensitivity ,rotation ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,coherence ,laser ,phase shift ,SU(2) ,excited state ,optical ,antimatter ,nonlinear ,group ,composite ,Pauli ,qubit ,performance - Abstract
In 1949, Ramsey's method of separated oscillating fields was proposed boosting over many decades metrological performances of atomic clocks and becoming the standard technique for very high precision spectroscopic measurements. A generalization of this interferometric method is presented replacing the two single coherent excitations by arbitrary composite laser pulses. The rotation of the state vector of a two-level system under the effect of a single pulse is described using the Pauli matrices basis of the SU(2) group. It is then generalized to multiple excitation pulses by a recursive Euler-Rodrigues-Gibbs algorithm describing a composition of rotations with different rotation axes. A general analytical formula for the phase-shift associated with the clock's interferometric signal is derived. As illustrations, hyper-clocks based on three-pulse and five-pulse interrogation protocols are studied and shown to exhibit nonlinear cubic and quintic sensitivities to residual probe-induced light-shifts. The presented formalism is well suited to derive and optimize composite phase-shifts produced by tailored quantum algorithms in order to design a new generation of optical frequency standards, qubit rotations with reduced ac Stark-shift distortion for quantum computation and robust engineering control of atomic interferences in AMO physics targeting ultra-high precision laser spectroscopy on cold matter and anti-matter.
- Published
- 2021
44. Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
- Author
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Jérôme Dubail, Pasquale Calabrese, Sara Murciano, Abdus Salam International Centre for Theoretical Physics [Trieste] (ICTP), SISSA MathLab [Trieste], Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (INFN, Sezione di Trieste), Istituto Nazionale di Fisica Nucleare (INFN), Laboratoire de Physique et Chimie Théoriques (LPCT), and Institut de Chimie du CNRS (INC)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Global Symmetries ,High Energy Physics - Theory ,Nuclear and High Energy Physics ,FOS: Physical sciences ,QC770-798 ,Quantum entanglement ,field theory ,01 natural sciences ,group: Lie ,High Energy Physics::Theory ,Entropy (classical thermodynamics) ,Physics - Statistical Mechanics ,Nuclear and particle physics. Atomic energy. Radioactivity ,0103 physical sciences ,entropy: entanglement ,Order (group theory) ,modular ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Equipartition theorem ,Mathematical physics ,Physics ,Quantum Physics ,Conformal Field Theory ,Statistical Mechanics (cond-mat.stat-mech) ,Field Theories in Lower Dimensions ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,010308 nuclear & particles physics ,Conformal field theory ,Lie group ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,Symmetry (physics) ,Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici ,symmetry: nonabelian ,SU(2) ,High Energy Physics - Theory (hep-th) ,algebra: representation ,Wess-Zumino-Witten model ,Irreducible representation ,Quantum Physics (quant-ph) - Abstract
We consider the problem of the decomposition of the R\'enyi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log\log L$ contribution to the R\'enyi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group., Comment: 31 pages, v2: minor changes
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- 2021
45. Nonnegatively curved five-manifolds with non-abelian symmetry.
- Author
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Simas, Fabio
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We classify compact simply-connected 5-dimensional manifolds which admit a metric of nonnegative curvature with a connected non-abelian group acting by isometries. We show that they are diffeomorphic to either $$\hbox {S}^{5}, \hbox {S}^{3} \times \hbox {S}^{2}$$ , the nontrivial $$\hbox {S}^{3}$$ -bundle over $$\hbox {S}^{2}$$ or the Wu-manifold, SU(3)/SO(3). This result is a consequence of our equivariant classification of all SO(3) and SU(2)-actions on compact simply-connected five-manifolds. In the case of positive curvature we obtain a partial classification. [ABSTRACT FROM AUTHOR]
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- 2016
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46. The minimum number of rotations about two axes for constructing an arbitrarily fixed rotation
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Mitsuru Hamada
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su(2) ,so(3) ,rotation ,Science - Abstract
For any pair of three-dimensional real unit vectors m^ and n^ with |m^Tn^|
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- 2014
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47. Mechanical Entropy and Its Implications
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Pharis E. Williams
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mechanical entropy ,entropy manifold ,geometry quantum echanics ,quantum gravity ,SU(2) ,SU(3) ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
Abstract: It is shown that the classical laws of thermodynamics require that mechanical systems must exhibit energy that becomes unavailable to do useful work. In thermodynamics, this type of energy is called entropy. It is further shown that these laws require two metrical manifolds, equations of motion, field equations, and Weyl's quantum principles. Weyl's quantum principle requires quantization of the electrostatic potential of a particle and that this potential be non-singular. The interactions of particles through these non-singular electrostatic potentials are analyzed in the low velocity limit and in the relativistic limit. It is shown that writing the two particle interactions for unlike particles allows an examination in two limiting cases: large and small separations. These limits are shown to have the limiting motions of: all motions are ABOUT the center of mass or all motion is OF the center of mass. The first limit leads to the standard Dirac equation. The second limit is shown to have equations of which the electroweak theory is a subset. An extension of the gauge principle into a five-dimensional manifold, then restricting the generality of the five-dimensional manifold by using the conservation principle, shows that the four-dimensional hypersurface that is embedded within the 5-D manifold is required to obey Einstein's field equations. The 5-D gravitational quantum equations of the solar system are presented.
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- 2001
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48. Rotations in Three Dimensions.
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Prajapati, Jyotindra C., López-Bonilla, J., and López-Vázquez, R.
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ROTATION groups , *CAYLEY-Hamilton theorem , *MATRICES (Mathematics) , *PARAMETER estimation , *MATHEMATICAL notation , *MATHEMATICAL models - Abstract
We exhibit that from Cayley-Hamilton's quaternionic expression or via the matrix relation of Olinde Rodrigues-Cartan, it is possible to construct 3-rotations. Besides, we obtained the generators for O(3) and SU(2). [ABSTRACT FROM PUBLISHER]
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- 2015
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49. Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
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Pomoni, Elli, Rabe, Randle, and Zoubos, Konstantinos
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Temperley-Lieb ,Bethe ansatz ,holomorphic ,gauge field theory, quiver ,superpotential ,Hamiltonian ,vacuum state ,membrane model ,SU(2) ,SU(3) ,spin, chain ,spectral ,symmetry, algebra ,magnon, dispersion relation - Abstract
This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $\mathcal{N}=2$ SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry algebra, defined by the $R$-matrix read off from the superpotential. This implies that when orbifolding the $\mathcal{N}=4$ symmetry algebra down to the $\mathcal{N}=2$ one and then marginaly deforming, the broken generators are not lost, but get upgraded to quantum generators. Importantly, we demonstrate that these chains are dynamical, in the sense that their Hamiltonian depends on a parameter which is dynamically determined along the chain. At one loop we map the holomorphic SU(3) scalar sector to a dynamical 15-vertex model, which corresponds to an RSOS model, whose adjacency graph can be read off from the gauge theory quiver/brane tiling. One scalar SU(2) sub-sector is described by an alternating nearest-neighbour Hamiltonian, while another choice of SU(2) sub-sector leads to a dynamical dilute Temperley-Lieb model. These sectors have a common vacuum state, around which the magnon dispersion relations are naturally uniformised by elliptic functions. Concretely, for the $\mathbb{Z}_2$ quiver theory we study these dynamical chains by solving the one- and two-magnon problems with the coordinate Bethe ansatz approach. We confirm our analytic results by numerical comparison with the explicit diagonalisation of the Hamiltonian for short closed chains.
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- 2021
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50. A novel background field approach to the confinement-deconfinement transition
- Author
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Duifje Maria van Egmond, Urko Reinosa, Julien Serreau, Matthieu Tissier, Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
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High Energy Physics - Theory ,Computer Science::Machine Learning ,deconfinement ,temperature: transition ,gauge fixing ,High Energy Physics::Lattice ,General Physics and Astronomy ,FOS: Physical sciences ,finite temperature ,Computer Science::Digital Libraries ,susceptibility ,Statistics::Machine Learning ,High Energy Physics - Lattice ,High Energy Physics - Phenomenology (hep-ph) ,SU(3) ,gluon: propagator ,lattice ,Landau gauge ,Polyakov loop ,[PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat] ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,High Energy Physics - Lattice (hep-lat) ,High Energy Physics - Phenomenology ,background field ,SU(2) ,High Energy Physics - Theory (hep-th) ,resummation ,gauge field theory: Yang-Mills ,[PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] ,infrared ,Computer Science::Mathematical Software - Abstract
We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with lattice results in the range $[0,2T_c]$., Comment: 13 pages, 5 figures
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- 2021
- Full Text
- View/download PDF
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