Search

We study a simple lattice model with local symmetry, whose construction is based on a crossed module of finite groups. Its dynamical degrees of freedom are associated both to links and faces of a four-dimensional lattice. In special limits the discussed model reduces to certain known topological quantum field theories. In this work we focus on its dynamics, which we study both analytically and using Monte Carlo simulations. We prove a factorization theorem which reduces computation of correlation functions of local observables to known, simpler models. This, combined with standard Krammers-Wannier type dualities, allows us to propose a detailed phase diagram, which form is then confirmed in numerical simulations. We describe also topological charges present in the model, its symmetries and symmetry breaking patterns. The corresponding order parameters are the Polyakov loop and its generalization, which we call a Polyakov surface. The latter is particularly interesting, as it is beyond the scope of the factorization theorem. As shown by the numerical results, expectation value of Polyakov surface may serve to detects all phase transitions and is sensitive to a value of the topological charge., Small revision before journal submission

Significance Propelled agents that align their orientations upon collisions can give rise to macroscopic order. Depending on the details of the agents’ collisions, this ordering process can lead to spatiotemporal patterns, including traveling polar waves and nematic lanes. Recent experiments suggest that such patterns can also coexist and dynamically interconvert. Here we propose a general mechanism for such a phenomenology, which is based on patterned-induced local symmetry breaking. We show that macroscopic order in active-matter systems is linked to spatiotemporal density patterns, which in turn can lead to local symmetry breaking if the agent density exceeds the relevant threshold values. Our study sheds light on the principles of pattern formation and the emergence of symmetry in biological active-matter systems., The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents and a key component in the structuring of many biological systems. The relationships between the ordering process and the underlying microscopic interactions have been extensively explored both experimentally and theoretically. While emerging patterns often show one specific symmetry (e.g., nematic lane patterns or polarized traveling flocks), depending on the symmetry of the alignment interactions patterns with different symmetries can apparently coexist. Indeed, recent experiments with an actomysin motility assay suggest that polar and nematic patterns of actin filaments can interact and dynamically transform into each other. However, theoretical understanding of the mechanism responsible remains elusive. Here, we present a kinetic approach complemented by a hydrodynamic theory for agents with mixed alignment symmetries, which captures the experimentally observed phenomenology and provides a theoretical explanation for the coexistence and interaction of patterns with different symmetries. We show that local, pattern-induced symmetry breaking can account for dynamically coexisting patterns with different symmetries. Specifically, in a regime with moderate densities and a weak polar bias in the alignment interaction, nematic bands show a local symmetry-breaking instability within their high-density core region, which induces the formation of polar waves along the bands. These instabilities eventually result in a self-organized system of nematic bands and polar waves that dynamically transform into each other. Our study reveals a mutual feedback mechanism between pattern formation and local symmetry breaking in active matter that has interesting consequences for structure formation in biological systems.

We show that minimal massive 3d gravity (MMG), as well as the topological massive gravity, are particular cases of a more general `minimal massive gravity' theory (with a single massive propagating mode) arising upon spontaneous breaking of a local symmetry in a Chern-Simons gravity based on a Hietarinta or Maxwell algebra. Similar to the MMG case, the requirements that the propagating massive mode is neither tachyon nor ghost and that the central charges of an asymptotic algebra associated with a boundary CFT are positive, impose restrictions on the range of the parameters of the theory., Comment: 30 pages, v.2: typos corrected comments and references added

A global symmetry of a quantum field theory is said to have an 't Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions. This applies to Lorentz symmetries with gravitational anomalies as well. For theories with perturbative anomalies, we demonstrate the obstruction by analyzing the Wess-Zumino consistency conditions and current Ward identities in the presence of a boundary. We then recast the problem in terms of symmetry defects and find the same conclusions for anomalies of discrete and orientation-reversing global symmetries, up to the conjecture that global gravitational anomalies, which may not be associated with any diffeomorphism symmetry, also forbid the existence of boundary conditions. This conjecture holds for known gravitational anomalies in $D \le 3$ which allows us to conclude the obstruction result for $D \le 4$., Comment: 45 pages, 4 figures

Tensor network states have been a very prominent tool for the study of quantum many-body physics, thanks to their physically relevant entanglement properties and their ability to encode symmetries. In the last few years, the formalism has been extended and applied to theories with local symmetries too---lattice gauge theories. In order to extract physical properties (such as expectation values and correlation functions of physical observables) out of such states, one has to use the so-called transfer operators, the local properties of which dictate the long-range behavior of the state. In this paper we study transfer operators of tensor network states (in particular, projected entangled pair states) of lattice gauge theories, and consider the implications of the local symmetry on their structure and properties. In particular, we study the implications on the computation of the Wilson loop---a nonlocal, gauge-invariant observable which is central to pure gauge theories, the long-range decay behavior of which probes the confinement or deconfinement of static charges. Using the symmetry, we show how to simplify the tensor contraction required for computing Wilson loop expectation values for such states, eliminate nonphysical parts of the tensors, and formulate conditions relating local properties (that is, of the tensors) to their decay fashion.

In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing of a Fujikawa prescription, leads to the construction of relativistic propagators that satisfy the Chapman-Kolmogorov identity. By means of a detailed topological analysis, we find three different relativistic propagators (orthochronous, space-like, and Feynman) which are obtained from the exclusive integration of paths within different sectors in Minkowski space. Finally, the connection of this approach to the Feynman checkerboard construction is explored., 14 pages, accepted for publication in PRD

International audience; The motion of active colloids is generally achieved through their anisotropy, as exemplified by Janus colloids. Recently, there was a growing interest in the propulsion of isotropic colloids, which requires some local symmetry breaking. Although several mechanisms for such propulsion were proposed, little is known about the role played by the interactions within the environment of the colloid, which can have a dramatic effect on its propulsion. Here, we propose a minimal model of an isotropic colloid in a bath of solute particles that interact with each other. These interactions lead to a spontaneous phase transition close to the colloid, to directed motion of the colloid over very long timescales and to significantly enhanced diffusion, in spite of the crowding induced by solute particles. We determine the range of parameters where this effect is observable in the model, and we propose an effective Langevin equation that accounts for it and allows one to determine the different contributions at stake in self-propulsion and enhanced diffusion.

Bundles of filaments are subject to geometric frustration: certain deformations (e.g. bending while twisted) require longitudinal variations in spacing between filaments. While bundles are common -- from protein fibers to yarns -- the mechanical consequences of longitudinal frustration are unknown. We derive a geometrically-nonlinear formalism for bundle mechanics, using a gauge-like symmetry under reptations along filament backbones. We relate force balance to orientational geometry and assess the elastic cost of frustration in twisted toroidal bundles., Comment: 9 pages, 3 figures

We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a ${D}_{2}$ local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.

We introduce a new image contrast mechanism for scanning transmission electron microscopy (STEM) that derives from the local symmetry within the specimen. For a given position of the electron probe on the specimen, the image intensity is determined by the degree of similarity between the exit electron intensity distribution and a chosen symmetry operation applied to that distribution. The contrast mechanism detects both light and heavy atomic columns and is robust with respect to specimen thickness, electron probe energy and defocus. Atomic columns appear as sharp peaks that can be significantly narrower than for STEM images using conventional disc and annular detectors. This fundamentally different contrast mechanism complements conventional imaging modes and can be acquired simultaneously with them, expanding the power of STEM for materials characterisation., 7 pages, 5 figures

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symmetry in the linear model becomes smaller in the action than the conventional one. Moreover, we analyze the resulting linear model in the $1/N$ leading order. Consequently, we find that the model has a critical coupling constant similar to bosonic models. In the weak coupling regime, the $U(1)$ local symmetry is broken but supersymmetry is never broken. In contrast to the bosonic case, it is impossible to find stable vacua in the strong coupling regime as far as in the $1/N$ leading order. These results are straightforwardly generalized to the case of the hermitian symmetric space., Comment: 1+22 pages, 2 figures; v2: a subsection, footnotes and a reference added; v3: references and comments added for section 1, published version

In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^+,\th)$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states and the correlation functions of the superprimaries., Comment: 30 pages

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green's function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS., Comment: 20 pages, 0 figure

In the last 2 decades, increasingly precise measurements have established that the cuprate high-temperature superconductors exhibit numerous ordering tendencies. In addition to the “big 2”—Neel antiferromagnetism (AF) and d -wave superconductivity (SC)—a variety of other orders have been observed, especially in the enigmatic “pseudogap” regime of the phase diagram. The term pseudogap denotes a suppression of the density of states between a doping-dependent crossover temperature, T * ( p ) , and the (lower) SC transition temperature, T c ( p ) . Thus, for doping less than p * ≈ 0.19 [above which T * ( p ) vanishes], the pseudogap is the “normal state” out of which SC emerges. Mukhopadhyay et al. (1), in PNAS, venture a bold proposition as to the origin of the pseudogap on the basis of a careful examination of high-resolution scanning tunneling spectroscopy on Bi2Sr2CaCu2O8+x (Bi-2212). They focus on 2 distinct forms of order: charge density wave (CDW), the breaking of lattice translation symmetry; and nematicity, the breaking of lattice rotational symmetry. Both of these have been identified in well-defined regimes of the phase diagrams of all hole-doped cuprates. By measuring tunneling conductance over a large field of view, performing a Fourier transform, and analyzing data from distinct regions of momentum space, Mukhopadhyay et al. identify energies Δ * , E m a x D , and E m a x N characterizing the pseudogap, CDW, and nematicity, respectively. Measured on samples whose doping spans the pseudogap regime, these energies are, within experimental error, identical. On the basis of this result, Mukhopadhyay et al. (1) argue that the pseudogap is a consequence of a tendency toward a unidirectional density wave that, if long-range–ordered, would break both translation and rotation symmetry. In the presence of disorder, translation symmetry breaking cannot … [↵][1]2To whom correspondence may be addressed. Email: samuel.lederer{at}gmail.com. [1]: #xref-corresp-1-1

We consider a flavoured $B-L$ gauge symmetry under which only the third generation fermions are charged. Such a symmetry can survive at low energies (~TeV) while still allowing for two superheavy right-handed neutrinos, consistent with neutrino masses via see-saw and leptogenesis. We describe a mechanism for generating Yukawa couplings in this model and also discuss the low-energy phenomenology. Interestingly, the new gauge boson could explain the recent hints of lepton universality violation at LHCb, with a gauge coupling that remains perturbative up to the Planck scale. Finally, we discuss more general $U(1)$ symmetries and show that there exist only two classes of vectorial $U(1)$ that are both consistent with leptogenesis and remain phenomenologically viable at low-energies., 7 pages, 3 figures; v2: version published in PLB

We show that the nonlinear $\sigma-$model in an asymptotically $AdS_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $\sigma-$model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear $\sigma-$model fields and changes the space-time metric, and it can be used to map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions., Comment: 11 pages, 1 figure, minor corrections included

We investigate the possibility to find an ultraviolet completion of the simple extensions of the Standard Model where baryon number is a local symmetry. In the context of such theories one can understand the spontaneous breaking of baryon number at the low scale and the proton stability. We find a simple theory based on SU(4)_C x SU(3)_L x SU(3)_R where baryon number is embedded in a non-Abelian gauge symmetry. We discuss the main features of the theory and the possible implications for experiments. This theory predicts stable colored and/or fractional electric charged fields which can give rise to very exotic signatures at the Large Hadron Collider experiments such as CMS and ATLAS. We further discuss the embedding in a gauge theory based on SU(4)_C x SU(4)_L x SU(4)_R which could define the way to achieve the unification of the gauge interactions at the low scale., Comment: new references, minor corrections, to appear in Physics Letters B

Lattice Gauge Theories form a very successful framework for studying nonperturbative gauge field physics, in particular in Quantum Chromodynamics. Recently, their quantum simulation on atomic and solid-state platforms has been discussed, aiming at overcoming some of the difficulties still faced by the conventional approaches (such as the sign problem and real time evolution). While the actual implementations of a lattice gauge theory on a quantum simulator may differ in terms of the simulating system and its properties, they are all directed at studying similar physical phenomena, requiring the measurement of nonlocal observables, due to the local symmetry of gauge theories. In this work, general schemes for measuring such nonlocal observables (Wilson loops and mesonic string operators) in general lattice gauge theory quantum simulators that are based merely on local operations are proposed.

Lead and tin-based chalcogenide semiconductors like PbTe or SnSe have long been known to exhibit an unusually low thermal conductivity that makes them very attractive thermoelectric materials. An apparently unrelated fact is that the excitonic bandgap in these materials increases with temperature, whereas for most semiconductors one observes the opposite trend. These two anomalous features are also seen in a very different class of photovoltaic materials, namely the halide-perovskites such as CsPbBr3. It has been previously proposed that emphanisis, a local symmetry-breaking phenomenon, is the one common origin of these unusual features. Discovered a decade ago, emphanisis is the name given to the observed displacement of the lead or the tin ions from their cubic symmetry ground state to a locally distorted phase at high temperature. This phenomenon has been puzzling because it is unusual for the high-temperature state to be of a lower symmetry than the degenerate ground state. Motivated by the celebrated vibration-inversion resonance of the ammonia molecule, we propose a quantum tunneling-based model for emphanisis where decoherence is responsible for the local symmetry breaking with increasing temperature. From the analytic expression of the temperature dependence of the tunnel splitting (which serves as an order parameter), we provide three-parameter fitting formulae which capture the observed temperature dependence of the ionic displacements as well as the anomalous increase of the excitonic bandgap in all the relevant materials., Comment: The following article has been submitted to Applied Physics Letters

A convenient scheme is presented for calculating potential energy of van der Waals interacting bilayer graphene and other similar 2D compounds. It is based on the notion of the existence of two types of local symmetry of carbon atoms ordering, a 3- and 6-fold one. Potential energy of an atom is expressed as a sum of contributions from rings of equidistant atoms on neighboring layer. Methods are described to compute the radius of rings of equidistant atoms and number of atoms they contain. Exact positions of atoms are found as well, allowing to apply the introduced method in modelling of anisotropic potentials and to be used when twisting between layers is present.

We demonstrate that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors (class DIII) can become gapless and insulating by a combination of random edge velocity and interaction. Such a gapless insulating edge breaks time-reversal symmetry inhomogeneously, and the local symmetry broken regions can be regarded as static mass potentials or dynamical Ising spins. In both limits, we find that such glassy Majorana edges are generically exponentially localized and trap Majorana zero modes. Interestingly, for a statistically time-reversal symmetric edge, the low-energy theory can be mapped to a Dyson model at zero energy, manifesting a diverging density of states and exhibiting marginal localization (i.e., a diverging localization length). Although the ballistic edge state transport is absent, the localized Majorana zero modes reflect the nontrivial topology in the bulk. Experimental signatures are also discussed., Comment: 8 pages, 2 figures, published version

A curious correspondence has been known between Landau models and non-linear sigma models: Reinterpreting the base-manifolds of Landau models as field-manifolds, the Landau models are transformed to non-linear sigma models with same global and local symmetries. With the idea of the dimensional hierarchy of higher dimensional Landau models, we exploit this correspondence to present a systematic procedure for construction of non-linear sigma models in higher dimensions. We explicitly derive $O(2k+1)$ non-linear sigma models in $2k$ dimension based on the parent tensor gauge theories that originate from non-Abelian monopoles. The obtained non-linear sigma models turn out to be Skyrme-type non-linear sigma models with $O(2k)$ local symmetry. Through a dimensional reduction of Chern-Simons tensor field theories, we also derive Skyrme-type $O(2k)$ non-linear sigma models in $2k-1$ dimension, which realize the original and other Skyrme models as their special cases. As a unified description, we explore Skyrme-type $O(d+1)$ non-linear sigma models and clarify their basic properties, such as stability of soliton configurations, scale invariant solutions, and field configurations with higher winding number., Comment: 1+54 pages, 4 figures, 2 tables, discussions added, typos corrected, to appear in NPB

The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss’s law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3–6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7,8, realized mappings onto effective models to integrate out either matter or electric fields9–12, or were limited to very small systems13–16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter–gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss’s law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators. Quantum simulation in a 71-site optical lattice certifies gauge invariance, showing how this essential property of lattice gauge theories can be maintained across a quantum phase transition.

We describe how Goldstone bosons of spontaneous symmetry breaking $G \to H$ can reproduce anomalies of UV theories under the symmetry group $G$ at the nonperturbative level. This is done by giving a general definition of Wess-Zumino-Witten terms in terms of the invertible field theories in $d+1$ dimensions which describe the anomalies of $d$-dimensional UV theories. The hidden local symmetry $\widehat H$, which is used to describe Goldstone bosons in coset construction $G/H$, plays an important role. Our definition also naturally leads to generalized $\theta$-angles of the hidden local gauge group $\widehat H$. We illustrate this point by ${\rm SO}(N_c)$ (or ${\rm Spin}(N_c)$) QCD-like theories in four dimensions., Comment: 19 pages, 2 figures; V2: minor corrections and references added; V3: minor improvement

We report the observation of an antipolar phase in cubic ${\mathrm{GaNb}}_{4}{\mathrm{S}}_{8}$ driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of ${\mathrm{Nb}}_{4}{\mathrm{S}}_{4}$ molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at ${T}_{\mathrm{JT}}=31\text{ }\text{ }\mathrm{K}$, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in the cubic phase above ${T}_{\mathrm{JT}}$. Based on the variety of structural polymorphs reported in lacunar spinels, also including ferroelectric phases, we argue that ${\mathrm{GaNb}}_{4}{\mathrm{S}}_{8}$ may be transformable to a ferroelectric state, which would further classify the observed antipolar phase as antiferroelectric.

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons., Comment: Minor changes

The local structure of NaTiSi$_{2}$O$_{6}$ is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that on warming the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning $\sim$6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems., Comment: 7 pages, 5 figures

We study the Hamiltonian dynamics of a five-dimensional Chern-Simons theory for the gauge algebra $C_5$ of Izaurieta, Rodriguez and Salgado, the so-called S$_H$-expansion of the 5D (anti-)de Sitter algebra (a)ds, based on the cyclic group $\mathbb{Z}_4$. The theory consists of a 1-form field containing the (a)ds gravitation variables and 1-form field transforming in the adjoint representation of (a)ds. The gravitational part of the action necessarily contains a term quadratic in the curvature, beyond the Einstein-Hilbert and cosmological terms, for any choice of the two independent coupling constants. The total action is also invariant under a new local symmetry, called "crossed diffeomorphisms", beyond the usual space-time diffeomorphisms. The number of physical degrees of freedom is computed. The theory is shown to be "generic" in the sense of Ba\~nados, Garay and Henneaux, i.e., the constraint associated to the time diffeomorphisms is not independent from the other constraints., Comment: 19 pages. Reference added. Small correction in Section 3, results unchanged. Published in Eur. Phys. J. C 80, 138 (2020). https://doi.org/10.1140

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns : the gauge symmetry Z 2 . This symmetry is present in physical problems from topological transitions to QCD, and controls the computational hardness of instances of spin-glasses. Here, we show how to design a neural network, and a dataset, able to learn this symmetry and to find compressed latent representations of the gauge orbits. Our method pays special attention to system-wrapping loops, the so-called Polyakov loops, known to be particularly relevant for computational complexity., 4 pages, 4 figures + appendices

Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations between Noether currents of distinct global symmetries that coincide on the local level, thus generalizing the well-known relationship $\vec L=\vec r\times\vec p$ between momentum $\vec p$ and angular momentum $\vec L$. As a byproduct, we find a natural interpretation for the discrepancy between the canonical and metric energy-momentum tensors in theories of particles with spin. A symmetric energy-momentum tensor can thus be obtained from the Noether procedure without adding any ad hoc corrections or imposing additional constraints such as gauge invariance in Maxwell's electrodynamics., 8 pages; pedagogical exposition of aspects of the Noether theorem in classical field theory; Author's Original of a paper to be published in Physica Scripta

In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenböck and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the general quadratic theory by studying the spectrum around Minkowski. The linear theory generally contains two symmetric rank-2 fields plus a 2-form and, consequently, extra gauge symmetries are required to obtain potentially viable theories., Atraccion del Talento Cientifico en Salamancaprogramme, MINECO FIS2014-52837-P FIS2016-78859-P, European Research Council (ERC) 801781, Swiss National Science Foundation (SNSF) 179740, Estonian Research Council PRF project PRG356, European Union (EU) CoE TK133, CANTATA COST (European Cooperation in Science and Technology) action, EU Framework Programme Horizon 2020 CA15117, Spanish Ministry of Economy and Competitiveness FPU15/02864

We construct a generalized EFT approach to dense compact-star matter that exploits the CCP for hadron-quark continuity at high density, hidden topology and hidden symmetries of QCD. No Landau-Ginzburg-Wilsonian-type phase transition is involved. The microscopic DoF of QCD possibly intervening at high baryonic density are traded in for fractionalized topological objects. Essential in the description are symmetries invisible in QCD in the matter-free vacuum: Scale symmetry, flavor local symmetry and parity-doubling. The partial emergence of scale symmetry is signaled by a dilatonic scalar in a "pseudo-conformal" structure. Flavor gauge symmetry manifests with the $\rho$ meson mass going toward a Wilsonian RGFP identified with the VMFP at which the gauge boson mass goes to zero. Parity doubling is to take place as the quasi-nucleon mass converges to the chiral invariant $m_0$. The theory accounts satisfactorily for all known properties of normal nuclear matter and makes certain predictions that are drastically different from what's available in the literature. In particular, it provides a topological mechanism, argued to be robust, for the cross-over from soft-to-hard EoS that predicts the star properties in overall agreement with the presently available data, including the maximum star mass $M_{max}\sim 2.3 M_\odot$ and the recent LIGO/Virgo GW data. What is most glaringly different from all other approaches known, however, is the prediction for the rapid convergence to a sound velocity of star $v_s^2\approx 1/3$ at a density $n\gsim 3 n_0$, far from the asymptotic density $\gsim 50n_0$ expected in pQCD. We interpret this to signal the onset of albeit approximate conformal symmetry in dense compact-star matter. The model developed here could bring out a new paradigm in nuclear/hadron physics, exploiting ideas in condensed matter physics, nuclear and particle physics and astrophysics., Comment: Version to appear in Progress in Particle and Nuclear Physics

Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly mind boggling length scales - from nanoparticles to galaxies. However, quantitative measurements of entropy change using calorimetry are predominantly macroscopic, with direct atomic scale measurements being exceedingly rare. Here for the first time, we experimentally quantify the polar configurational entropy (in meV/K) using sub-\r{a}ngstr\"{o}m resolution aberration corrected scanning transmission electron microscopy. This is performed in a single crystal of the prototypical ferroelectric $\mathsf{LiNbO_3}$ through the quantification of the niobium and oxygen atom column deviations from their paraelectric positions. Significant excursions of the niobium - oxygen polar displacement away from its symmetry constrained direction is seen in single domain regions which increases in the proximity of domain walls. Combined with first principles theory plus mean field effective Hamiltonian methods, we demonstrate the variability in the polar order parameter, which is stabilized by an increase in the magnitude of the configurational entropy. This study presents a powerful tool to quantify entropy from atomic displacements and demonstrates its dominant role in local symmetry breaking at finite temperatures in classic, nominally Ising ferroelectrics., Comment: 23 pages, 21 figures (5 main, 16 supplemental)

Interest in substitutional disordered alloys has recently reemerged with focus on the symmetry-sensitive properties in the alloy such as topological insulation and Rashba effect. A substitutional random alloy manifests a distribution of local environments, creating a polymorphous network. While the macroscopic average (monomorphous) structure may have the original high symmetry of the constituent compounds, many observable physical properties are sensitive to local symmetry, and are hence $$ rather than $P(S_0)$=$P()$. The fundamental difference between polymorphous $$ and monomorphous $P(S_0)$ led to the often-diverging results and the missing the atomic-scale resolution needed to discern symmetry-related physics. A natural approach capturing the polymorphous aspect is supercell model, which however suffers the difficulty of band folding ('spaghetti bands'), rendering the E vs k dispersion needed in topology and Rashba physics and seen in experiments, practically inaccessible. A solution that retains the polymorphous nature but restores the E vs k relation is to unfold the supercell bands. This yields alloy Effective Band Structure (EBS), providing a 3D picture of spectral density consisting of E- and k-dependent spectral weight with coherent and incoherent features, all created naturally by the polymorphous distribution of many local environments. We illustrate this EBS approach for CdTe-HgTe, PbSe-SnSe and PbS-PbTe alloys. We found properties that are critical for e.g. topological phase transition and Rashba splitting but totally absent in conventional monomorphous approaches, including (1) co-existing, wavevector- and energy-dependent coherent band splitting and incoherent band broadening, (2) coherent-incoherent transition along different k space directions, and (3) Rashba-like band splitting having both coherent and incoherent features., Comment: 17 pages, 8 figures, 1 table

We reconsider a scenario in which photons and other gauge fields appear as the composite vector bosons made of the fermion pairs that may happen with or without spontaneous violation of Lorentz invariance. The class of composite models for emergent gauge fields is proposed, where these fields are required to be restricted by by the nonlinear covariant constraint of type $ A_{\mu }^{2}=M^{2}$. Such a constraint may only appear if the corresponding fermion currents in the prototype model, being invariant under some global internal symmetry $G$, are properly constrained as well. In contrast to the conventional approach, the composite bosons emerged in this way appear naturally massless, the global symmetry $G$ in the model turns into the local symmetry $G_{loc}$, while the vector field constraint reveals itself as the gauge fixing condition. Finally, we consider the case when the constituent fermions generating emergent gauge bosons could be at the same time the preons composing the known quark-lepton species in the Standard Model and Grand Unified Theories., Comment: 15 pages, Published version - to appear in Physics Letters B. arXiv admin note: text overlap with arXiv:1305.6898

Lead halide perovskites such as methylammonium lead triiodide (MAPI) have outstanding optical and electronic properties for photovoltaic applications, yet a full understanding of how this solution processable material works so well is currently missing. Previous research has revealed that MAPI possesses multiple forms of static disorder regardless of preparation method, which is surprising in light of its excellent performance. Using high energy resolution inelastic X-ray (HERIX) scattering, we measure phonon dispersions in MAPI and find direct evidence for another form of disorder in single crystals: large amplitude anharmonic zone-edge rotational instabilities of the PbI_6 octahedra that persist to room temperature and above, left over from structural phase transitions that take place tens to hundreds of degrees below. Phonon calculations show that the orientations of the methylammonium couple strongly and cooperatively to these modes. The result is a non-centrosymmetric, instantaneous local structure, which we observe in atomic pair distribution function (PDF) measurements. This local symmetry breaking is unobservable by Bragg diffraction, but can explain key material properties such as the structural phase sequence, ultra low thermal transport, and large minority charge carrier lifetimes despite moderate carrier mobility., 30 pages, 11 figures

In pure gravity mediation (PGM), the most minimal scheme for the mediation of supersymmetry (SUSY) breaking to the visible sector, soft masses for the standard model gauginos are generated at one loop rather than via direct couplings to the SUSY-breaking field. In any concrete implementation of PGM, the SUSY-breaking field is therefore required to carry nonzero charge under some global or local symmetry. As we point out in this note, a prime candidate for such a symmetry might be B-L, the Abelian gauge symmetry associated with the difference between baryon number B and lepton number L. The F-term of the SUSY-breaking field then not only breaks SUSY, but also B-L, which relates the respective spontaneous breaking of SUSY and B-L at a fundamental level. As a particularly interesting consequence, we find that the heavy Majorana neutrino mass scale ends up being tied to the gravitino mass, Lambda_N ~ m_3/2. Assuming nonthermal leptogenesis to be responsible for the generation of the baryon asymmetry of the universe, this connection may then explain why SUSY necessarily needs to be broken at a rather high energy scale, so that m_3/2 >~ 1000 TeV in accord with the concept of PGM. We illustrate our idea by means of a minimal model of dynamical SUSY breaking, in which B-L is identified as a weakly gauged flavor symmetry. We also discuss the effect of the B-L gauge dynamics on the superparticle mass spectrum as well as the resulting constraints on the parameter space of our model. In particular, we comment on the role of the B-L D-term., 25 pages, 1 figure

The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $\overline{SL(2,\mathbb C)}$ currents. This naturally gives rise to a $\overline{SL(2,\mathbb C)}$ current algebra living on the celestial sphere. The generators of the $\overline{SL(2,\mathbb C)}$ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An $n$ point MHV amplitude satisfies two systems of $(n-2)$ linear first order PDEs corresponding to $(n-2)$ positive helicity gravitons. We have checked, using Hodges' formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations. This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of $2$-D CFT., Final JHEP Version

Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent., Comment: 7 pages; version accepted for publication in Phys. Lett. B; a table, footnotes, references, and comments added

In recent work Alexandre, Ellis, Millington and Seynaeve have extended the Goldstone theorem to non-Hermitian Hamiltonians that possess a discrete antilinear symmetry such as $PT$. They restricted their discussion to those realizations of antilinear symmetry in which all the energy eigenvalues of the Hamiltonian are real. Here we extend the discussion to the two other realizations possible with antilinear symmetry, namely energies in complex conjugate pairs or Jordan-block Hamiltonians that are not diagonalizable at all. In particular, we show that under certain circumstances it is possible for the Goldstone boson mode itself to be one of the zero-norm states that are characteristic of Jordan-block Hamiltonians. While we discuss the same model as Alexandre et al. our treatment is quite different, though their main conclusion that one can have Goldstone bosons in the non-Hermitian case remains intact. In their paper Alexandre et al. presented a variational procedure for the action in which the surface term played an explicit role, to thus suggest that one has to use such a procedure in order to establish the Goldstone theorem in the non-Hermitian case. However, by taking certain fields that they took to be Hermitian to actually either be anti-Hermitian or be made so by a similarity transformation, we show that we are then able to obtain a Goldstone boson using a completely standard variational procedure. Since we use a standard variational procedure we can readily extend our analysis to a continuous local symmetry by introducing a gauge boson. We show that when we do this the gauge boson acquires a non-zero mass by the Higgs mechanism in all realizations of the antilinear symmetry, except the one where the Goldstone boson itself has zero norm, in which case, and despite the fact that the continuous local symmetry has been spontaneously broken, the gauge boson remains massless., 21 pages, revtex4. Final version, Phys. Rev D 99, 045006 (2019). Title of paper changed in journal

The canonical quantization of a massive symmetric rank-two tensor in string theory, which contains two Stueckelberg fields, was studied. As a preliminary study, we performed a canonical quantization of the Proca model to describe a massive vector particle that shares common properties with the massive symmetric rank-two tensor model. By performing a canonical analysis of the Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian possesses only first class constraints that generate local gauge transformation. By explicit calculations, we show that the massive symmetric rank-two tensor theory is gauge invariant only in the critical dimension of open bosonic string theory, i.e., $d=26$. This emphasizes that the origin of local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST) operator, which is valid only in the critical dimension. For a particular gauge imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle. Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two particles with small masses, we propose the transverse-traceless (TT) gauge to quantize the SZ model as an alternative gauge condition. In the TT gauge, the two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and integrated trivially. The massive spin-two particle can be described by the SZ model in the TT gauge, where the propagator of the massive spin-two particle has a well-defined massless limit., 16 pages, 1 figure

We clarify and extend further the idea developed in \cite{PKLMR,MLPR} that baryonic matter at high density has an emergent "pseudo-conformal symmetry." It is argued that as baryonic density exceeds $n \simeq n_{1/2} \gtrsim 2n_0$, a topology change mimicking the baryon-quark continuity takes place at $n_{1/2}$. In terms of skyrmions, this corresponds to the transition from skyrmions to half-skyrmions and impacts on the equation of state of dense baryonic matter. The emergence in medium at $n_{1/2}$ of parity-doublet symmetry -- which is invisible in QCD in matter-free vacuum -- plays the crucial role. The consequence of the topology change is that massive compact stars carry the "pseudo-conformal sound velocity" $v_s^2/c^2\approx 1/3$ at $n\gsim n_{1/2}$ signaling a precursor to precocious emergence of scale symmetry as well as {a} local symmetry hidden in QCD in the matter-free vacuum. A highly significant prediction of this work is that the topology change density from normal matter to half-skyrmion matter, up-to-date inaccessible either by QCD proper or by terrestrial experiments, could possibly be pinned down within the range $2 < n_{1/2}/n_0 < 4$, commensurate with the range expected for a continuous hadrons-to-quarks/gluons transition., Version published in Phys. Rev. D

In earlier papers (Leblond et.al., 2011, 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a "double'' propagation criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed., Comment: 33 pages, 10 figures

In contrast to the idealized scenario of perfect global symmetries that is notoriously elusive, local symmetries [1] abound in nature. Prominent examples include quasicrystals [2], macromolecules [3] and tailored photonic multilayer-systems [4]. Since the Hamiltonian of a locally symmetric system does, in general, not commute with the local symmetry operation, even though the potential remains invariant under the respective transformation, tracking the influence on a system's dynamics can be challenging. A promising approach is the non-local continuity formalism that can readily be applied to discrete systems governed by a Schrodinger equation [5]. It relates a non-local charge Σ 0 to the non-local boundary current q dD in each symmetry domain. For arrangements without on-site asymmetry, the continuity equation reads ∂ z Σ D = q dD , where ∂ z is the derivative in propagation direction. In this vein, we can readily distinguish locally symmetric structures from both fully non-symmetric systems on the one hand, and globally symmetric structures on the other. Notably, an experimental demonstration of this continuity equation has remained elusive so far.

In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well known instability of coplanar crack propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double propagation criterion combining Griffith's energetic condition and principle of local symmetry. Under such assumptions instability modes were indeed evidenced for values of the mode mixity ratio of the mode III to mode I stress intensity factors applied remotely larger than some threshold depending only on Poisson's ratio. Unfortunately, the predicted thresholds were much larger than those generally observed for typical values of this material parameter. While the subcritical character of the nonlinear bifurcation from coplanar to fragmented fronts has been proposed as a possible explanation for this discrepancy (Chen et al., 2015), we propose here an alternative explanation based on the introduction of a constitutive relationship between the fracture energy and the mode mixity ratio, which is motivated by experimental observations. By reexamining the linear stability analysis of a planar propagating front, we show that such a relationship suffices, provided that it is strong enough, to lower significantly the threshold value of the mode mixity ratio for instability so as to bring it in a range more consistent with experiments. Interesting formulae are also derived for the distributions of the perturbed stress intensity factors and energy release rate, in the special case of perturbations of the crack surface and front obeying the principle of local symmetry and having reached a stationary state., Comment: 30 pages and 7 figures

An attempt is made to bring into harmony two of the paradigms commonly used in the theory of continuous distributions of defects. It is shown that the common differential geometric apparatus is provided neatly by the theory of G-structures. In the case of a structural model, based on putative experimental observations at the microscopic level, a G-structure can be shown to emerge from the group of linear transformations that preserve a tensorial quantity. For the phenomenological (macroscopic) constitutive model, the G-structure arises from the notion of material isomorphism and the underlying local symmetry group of the constitutive law. A comparative example is presented in the framework of certain smectic liquid crystals.

We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the second-order derivative of the scalar is absorbed into the projective gauge mode when the unitary gauge can be imposed. Incidentally, the connection does not have the kinetic term in these theories and then it is just an auxiliary field. We can thus (at least in principle) integrate the connection out and obtain a form of scalar-tensor theories in the Riemannian geometry. The projective symmetry then hides in the ghost-free scalar-tensor theories. As an explicit example, we show the relationship between the quadratic order scalar-metric-affine theory and the quadratic U-degenerate theory. The explicit correspondence between the metric-affine (Palatini) formalism and the metric one could be also useful for analyzing phenomenology such as inflation., Comment: 15 pages, no figure, published version

We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of $\alpha$-helices and $\beta$-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the negative normal of the chain, to mimic the presence of side chains in real proteins. This leads to the emergence of a novel phase within the previously obtained marginally compact phase, with the appearance of more complex secondary structure assemblies. The potential importance of this new phase in the \textit{de novo} design of self-assembled peptides is highlighted., Comment: 25 pages, 19 figures. supplementary materials at https://pubs.rsc.org/en/content/articlelanding/2019/sm/c9sm00851a/unauth#!divAbstract

We calculate the meson spectrum of the Sp(4) lattice gauge theory coupled to two fundamental flavours of dynamical Dirac fermions. We focus on some of the lightest (flavoured) spin-0 and spin-1 states. This theory provides an ultraviolet completion for composite Higgs models based upon the SU(4)/Sp(4) coset. We analyse the strongly coupled dynamics in isolation, without explicit coupling to the standard model. We carry out continuum extrapolations using dynamical ensembles generated at five different values of bare lattice coupling, and for several values of the bare fermion mass. We fit the resulting meson masses and decay constants to a low-energy effective field theory built along the ideas of hidden local symmetry. We also compare our results to those of other closely related lattice gauge theories, which have matter content consisting of two fundamental Dirac flavours., Comment: 7 pages, 1 table, 4 figures, Contribution to the 37th International Symposium on Lattice Field Theory - LATTICE2019, 16-22 June 2019, Wuhan, China

Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning models for prediction of DFT calculated properties are currently of interest. A particular challenge for \emph{new} materials is that the atomic positions are generally not known. We present a machine learning model for the prediction of DFT-calculated formation energies based on Voronoi quotient graphs and local symmetry classification without the need for detailed information about atomic positions. The model is implemented as a message passing neural network and tested on the Open Quantum Materials Database (OQMD) and the Materials Project database. The test mean absolute error is 20 meV on the OQMD database and 40 meV on Materials Project Database. The possibilities for prediction in a realistic computational screening setting is investigated on a dataset of 5976 ABSe$_3$ selenides with very limited overlap with the OQMD training set. Pretraining on OQMD and subsequent training on 100 selenides result in a mean absolute error below 0.1 eV for the formation energy of the selenides., Comment: 14 pages including references and 13 figures