Gauge Symmetry Research Articles

Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} × \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

A model of pseudo-Nambu-Goldstone dark matter with two complex scalars

Pseudo-Nambu-Goldstone (pNG) dark matter (DM) is a promising DM candidate and able to explain the measured DM abundance by the thermal freeze-out mechanism evading the stringent bound from DM direct detection experiments. We propose a new model providing a pNG DM by introducing two Standard-Model-singlet complex scalars with the same charges of a dark U(1) gauge symmetry. They are also charged under a U(1) global symmetry corresponding to their relative phase rotations, which is explicitly broken by a soft-breaking term in the scalar potential. The both U(1) symmetries are spontaneously broken by their vacuum expectation values, giving rise to one real pNG boson. We also introduce a discrete ℤ2 symmetry exchanging the two scalars to stabilize the pNG boson as DM. It is shown that this model reproduces the DM abundance consistently with the current bound from the direct detection experiments. The model has a gauge kinetic mixing between the dark and U(1)Y gauge fields, which allows the dark gauge boson to decay even with a relatively light mass and prevents it from being an additional DM component. The Landau pole is avoided thanks to the small gauge coupling constant. In addition, a DM pair dominantly annihilates into a pair of the dark gauge bosons if the gauge boson mass is lighter than the DM mass, and thus its cross section has significantly different parameter dependence from other pNG DM models. We also calculate the DM-nucleon scattering cross section at the loop level. It turns out that it is necessary to probe region covered by the neutrino fog in order to test this model.

Measurement of the superfluid fraction of a supersolid by Josephson effect.

A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising1-12. It might be related to the supersolid phase of matter, in which the spontaneous breaking of gauge and translational symmetries leads to a spatially modulated macroscopic wavefunction13-16. This relation was recognized only in some cases1,2,5-9 and there is the need for a universal property quantifying the differences between supersolids and ordinary matter, such as the superfluid fraction, which measures the reduction in superfluid stiffness resulting from the spatial modulation16-18. The superfluid fraction was introduced long ago16, but it has not yet been assessed experimentally. Here we demonstrate an innovative method to measure the superfluid fraction based on the Josephson effect, a ubiquitous phenomenon associated with the presence of a physical barrier between two superfluids or superconductors19, which might also be expected for supersolids20, owing to the spatial modulation. We demonstrate that individual cells of a supersolid can sustain Josephson oscillations and we show that, from the current-phase dynamics, we can derive directly the superfluid fraction. Our study of a cold-atom dipolar supersolid7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents16-18. Our results open a new direction of research that may unify the description of all supersolid-like systems.

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

Bloch Gauge symmetry of the semiconductor Bloch equations

Bloch Gauge symmetry of the semiconductor Bloch equations

Hunting WIMPs with LISA: correlating dark matter and gravitational wave signals

The thermal freeze-out mechanism in its classical form is tightly connected to physics beyond the Standard Model around the electroweak scale, which has been the target of enormous experimental efforts. In this work we study a dark matter model in which freeze-out is triggered by a strong first-order phase transition in a dark sector, and show that this phase transition must also happen close to the electroweak scale, i.e. in the temperature range relevant for gravitational wave searches with the LISA mission. Specifically, we consider the spontaneous breaking of a U(1)′ gauge symmetry through the vacuum expectation value of a scalar field, which generates the mass of a fermionic dark matter candidate that subsequently annihilates into dark Higgs and gauge bosons. In this set-up the peak frequency of the gravitational wave background is tightly correlated with the dark matter relic abundance, and imposing the observed value for the latter implies that the former must lie in the milli-Hertz range. A peculiar feature of our set-up is that the dark sector is not necessarily in thermal equilibrium with the Standard Model during the phase transition, and hence the temperatures of the two sectors evolve independently. Nevertheless, the requirement that the universe does not enter an extended period of matter domination after the phase transition, which would strongly dilute any gravitational wave signal, places a lower bound on the portal coupling that governs the entropy transfer between the two sectors. As a result, the predictions for the peak frequency of gravitational waves in the LISA band are robust, while the amplitude can change depending on the initial dark sector temperature.

Gauge symmetry of excited states in projected entangled-pair state simulations

Gauge symmetry of excited states in projected entangled-pair state simulations

Unimodular proca theory: breaking the U(1) gauge symmetry of unimodular gravity via a mass term

We study the Hamiltonian structure of unimodular-like theories, where the cosmological constant (or other supposed constants of nature) are demoted from fixed parameters to classical constants of motion. No new local degrees of freedom are present as a result of a U(1) gauge invariance of the theory. Hamiltonian analysis of the action reveals that the only possible gauge fixing that can be enforced is setting the spatial components of the four-volume time vector Ti≈0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{T}^{i}\\approx 0$$\\end{document}. As a consequence of this, the gauge-fixed unimodular path integral is equivalent to the minisuperspace unimodular path integral. However, should we break the U(1) gauge invariance, two things happen: a massless propagating degree of freedom appears, and the (gauge-invariant) zero-mode receives modified dynamics. The implications are investigated, with the phenomenology depending crucially on the target “constant”.

Emergent gauge symmetry in active Brownian matter

Emergent gauge symmetry in active Brownian matter

Darboux’s Theorem, Lie series and the standardization of the Salerno and Ablowitz–Ladik models

In the framework of nonlinear Hamiltonian lattices, we revisit the proof of Moser-Darboux’s Theorem, in order to present a general scheme for its constructive applicability to Hamiltonian models with non-standard symplectic structures. We take as a guiding example the Salerno and Ablowitz–Ladik (AL) models: we justify the form of a well-known change of coordinates which is adapted to the Gauge symmetry, by showing that it comes out in a natural way within the general strategy outlined in the proof. Moreover, the full or truncated Lie-series technique in the extended phase-space is used to transform the Salerno model, at leading orders in the Darboux coordinates: thus the dNLS Hamiltonian turns out to be a normal form of the Salerno and AL models; as a byproduct we also get estimates of the dynamics of these models by means of dNLS one. We also stress that, once it is cast into the perturbative approach, the method allows to deal with the cases where the explicit trasformation is not known, or even worse it is not writable in terms of elementary functions.

Quantization of linear acoustic and elastic wave models in characterizations of isomorphism

From the macroscopic to the microscopic world, quantum mechanical effects in acoustics and elastic waves have become increasingly important. Observations on the quantum effects of acoustic and elastic waves using experimental methods have been reported in the literature. However, the conventional formulations of acoustic and elastic waves are still mainly governed by classical models. In this study, we investigated the quantization of acoustic and elastic waves using generalized Lorenz gauges. The potential variables of acoustic and elastic waves can be quantized in a manner similar to that of electrodynamics. The results include the Schrödinger equation with minimal coupling between the field and particles. The quantization of field variables is established as a consequence of the gauge symmetry property of the Schrödinger equation. Later, we explored the connections between the parallel formulations of mechanics and waves through an algebraic aspect. This highlights the isomorphism pattern from the theoretical characterization within the parallel formulations. To support the results, the derivations of potential formulations based on Lorenz gauges and functional mapping between field variables are presented.

Asymptotic ultraviolet-safe unification of gauge and Yukawa couplings: The exceptional case

The ultimate dream of unification models consists in combining both gauge and Yukawa couplings into one unified coupling. This is achieved by using a supersymmetric exceptional E6 gauge symmetry together with asymptotic unification in compact five-dimensional space-time. The ultraviolet fixed point requires exactly three fermion generations: one in the bulk, and the two light ones localised on the SO(10) boundary in order to cancel gauge anomalies. A second option allows to preserve baryon number and to lower the compactification scale down to the typical scales of the intermediate Pati-Salam gauge theory.

The QCD axion sum rule

We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides the η′). We determine the exact mathematical condition for an arbitrary N-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among the N axion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{N} $$\\end{document} at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associated N − 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.

Modelling ductile damage in metals and alloys through Weyl condition exploiting local gauge symmetries

Local translational and scaling symmetries in space–time is exploited for modelling ductile damage in metals and alloys over wide ranges of strain rate and temperature. The invariant energy density corresponding to the ductile deformation is constructed through the gauge invariant curvature tensor by imposing the Weyl like condition. In contrast, the energetics of the plastic deformation is brought in through the gauge compensating field emerged due to local translation and attempted to explore the geometric interpretation of certain internal variables often used in classical viscoplasticity models. Invariance of the energy density under the local action of translation and scaling is preserved through minimally replaced space–time gauge covariant operators. Minimal replacement introduces two non-trivial gauge compensating fields pertaining to local translation and scaling. These are used to describe ductile damage, including plastic flow and micro-crack evolution in the material. A space–time pseudo-Riemannian metric is used to lay out the kinematics in a finite-deformation setting. Recognizing the available insights in classical theories of viscoplasticity, we also establish a correspondence of the gauge compensating field due to spatial translation with Kröner’s multiplicative decomposition of the deformation gradient. Thermodynamically consistent coupling between viscoplasticity and ductile damage is ensured through an appropriate degradation function. Non-ordinary state-based (NOSB) peridynamics (PD) discretization of the model is used for numerical implementation. We conduct simulations of uniaxial deformation to validate the model against available experimental evidence and to assess its predictive features. The model’s viability is tested in reproducing a few experimentally known facts, viz., strain rate locking in the stress–strain response, whose origin is traced to a nonlinear microscopic inertia term arising out of the space–time translation symmetry. Finally, we solved 2D and axisymmetric deformation problems for qualitatively validating the model’s viability. NOSB peridynamics axisymmetric formulation in finite deformation setup is also presented.

Predictive Dirac neutrino spectrum with strong CP solution in SU(5)L × SU(5)R unification

We develop a grand unified theory of matter and forces based on the gauge symmetry SU(5)L × SU(5)R with parity interchanging the two factor groups. Our main motivation for such a construction is to realize a minimal GUT embedding of left-right symmetric models that provide a parity solution to the strong CP problem without the axion. We show how the gauge couplings unify with an intermediate gauge symmetry SU(3)cL × SU(2)2L × U(1)L × SU(5)R, and establish its consistency with proton decay constraints. The model correctly reproduces the observed fermion masses and mixings and leads to naturally light Dirac neutrinos with their Yukawa couplings suppressed by a factor MI/MG, the ratio of the intermediate scale to the GUT scale. We call this mechanism type II-Dirac seesaw. Furthermore, the model predicts δCP = ±(130.4±1.2)° and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${m}_{{\ u }_{1}}$$\\end{document} = (4.8 – 8.4) meV for the Dirac CP phase and the lightest neutrino mass. We demonstrate how the model solves the strong CP problem via parity symmetry.

Superspin chains solutions from 4D Chern-Simons theory

As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge symmetry. The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by A(m − 1 | n − 1), B(m | n), C(n) and D(m | n).

The global B − L symmetry in the flavor-unified SU(N) theories

We study the origin of the global B − L symmetry in a class of flavor-unified theories with gauge groups of SU(N ≥ 6). In particular, we focus on the SU(8) theory which can minimally embed three-generational SM fermions non-trivially. A reformulation of the third law for the flavor sector proposed by Georgi is useful to manifest the underlying global symmetries. The ’t Hooft anomaly matching and the generalized neutrality conditions for Higgs fields play the key roles in defining the B − L symmetry. Based on the global B − L symmetry, we count the Higgs fields that can develop the VEVs and the massless sterile neutrinos in the SU(8) theory. We also prove that a global B − L symmetry can always be defined in any SU(N ≥ 6) theory when it is spontaneously broken to the SM gauge symmetry.

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1))H3(G,U(1))×H2(G,U(1)). The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Chiral Gauge Theory at the Boundary between Topological Phases.

I demonstrate how chiral fermions with an exact gauge symmetry can appear on the d-dimensional boundary of a finite volume (d+1)-dimensional manifold, without any light mirror partners. The condition for the d-dimensional boundary theory to be local is that gauge anomalies cancel and that the volume be large. This can likely be achieved on a lattice and provides a new paradigm for the lattice regularization of chiral gauge theories.

PTOLEMY's test of generalized neutrino interactions: unveiling challenges and constraints

Unanswered questions surrounding neutrinos have motivated investigations into physics beyond the standard model (SM) of particle physics. In particular, generalized neutrino interactions (GNI) provide a broader framework for studying these effects compared to the commonly studied non-standard neutrino interactions. These interactions are described by higher dimensional operators while maintaining the gauge symmetries of the SM. Furthermore, the cosmic neutrino background, a predicted component of the SM and standard cosmology, has yet to be directly detected. To shed light on this elusive phenomenon, we conduct a comprehensive analysis of the relevant GNI, specifically focusing on their implications for the proposed cosmic neutrino detector PTOLEMY. We make an attempt to see the capabilities and the limitations of PTOLEMY in sensing GNI while remaining optimistic regarding PTOLEMY's experimental resolution. These interactions play a significant role in modifying the electron spectrum resulting from the capture of cosmic neutrinos on radioactive tritium. This work also explores how the presence of these interactions influences the differential electron spectrum, taking into account factors such as finite experimental resolution, the mass of the lightest neutrino eigenstate, the strength of the interactions, and the ordering of neutrino mass.