Gauge Symmetry Research Articles

Scotogenic gauge mechanism for neutrino mass and dark matter

Scotogenic is a scheme for neutrino mass generation through the one-loop contribution of an inert scalar doublet and three sterile neutrinos. This work argues that such inert scalar doublet is a Goldstone boson mode associated with a gauge symmetry breaking. Hence, the resultant scotogenic gauge mechanism is very predictive, generating neutrino mass as contributed by a new gauge boson doublet that eats such Goldstone bosons. The dark matter stability is manifestly ensured by a matter parity as residual gauge symmetry for which a vector dark matter candidate is hinted.

A closer look in the mirror: reflections on the matter/dark matter coincidence

We argue that the striking similarity between the cosmic abundances of baryons and dark matter, despite their very different astrophysical behavior, strongly motivates the scenario in which dark matter resides within a rich dark sector parallel in structure to that of the standard model. The near cosmic coincidence is then explained by an approximate ℤ2 exchange symmetry between the two sectors, where dark matter consists of stable dark neutrons, with matter and dark matter asymmetries arising via parallel WIMP baryogenesis mechanisms. Taking a top-down perspective, we point out that an adequate ℤ2 symmetry necessitates solving the electroweak hierarchy problem in each sector, without our committing to a specific implementation. A higher-dimensional realization in the far UV is presented, in which the hierarchical couplings of the two sectors and the requisite ℤ2-breaking structure arise naturally from extra-dimensional localization and gauge symmetries. We trace the cosmic history, paying attention to potential pitfalls not fully considered in previous literature. Residual ℤ2-breaking can very plausibly give rise to the asymmetric reheating of the two sectors, needed to keep the cosmological abundance of relativistic dark particles below tight bounds. We show that, despite the need to keep inter-sector couplings highly suppressed after asymmetric reheating, there can naturally be order-one couplings mediated by TeV scale particles which can allow experimental probes of the dark sector at high energy colliders. Massive mediators can also induce dark matter direct detection signals, but likely at or below the neutrino floor.

Gravitational Waves from First-Order Phase Transition in an Electroweakly Interacting Vector Dark Matter Model

Abstract We discuss gravitational waves (GWs) in an electroweakly interacting vector dark matter (DM) model. In the model, the electroweak gauge symmetry is extended to SU(2)$_0 \times$SU(2)$_1 \times$SU(2)$_2 \times$U(1)$_Y$ and spontaneously broken into SU(2)$_L \times$U(1)$_Y$ at TeV scale. The model has an exchange symmetry between SU(2)$_0$ and SU(2)$_2$. This symmetry stabilizes some massive vector bosons associated with the spontaneous symmetry breaking described above, and an electrically neutral one is a DM candidate. In a previous study, it was found that the gauge couplings of SU(2)$_0$ and SU(2)$_1$ are relatively large to explain the measured value of the DM energy density via the freeze-out mechanism. With the large gauge couplings, the gauge bosons potentially have a sizable effect on the scalar potential. In this paper, we focus on the phase transition of SU(2)$_0 \times$SU(2)$_1 \times$SU(2)$_2 \rightarrow$ SU(2)$_L$. We calculate the effective potential at finite temperature and find that the phase transition is first-order and strong in a wide range of the parameter space. The strong first-order phase transition generates GWs. We calculate the GW spectrum and find that it will be possible to detect the GWs predicted in the model by future space-based GW interferometers. We explore the regions of the parameter space probed by the GW detection. We find that the GW detection can probe the region where the mass of $h^{\prime }$, a CP-even scalar in the model, is a few TeV.

Phenomenological aspects of the fermion and scalar sectors of a S4 flavored 3-3-1 model

We proposed a viable and predictive model based on the SU(3)C×SU(3)L×U(1)X gauge symmetry, supplemented by the global U(1)Lg symmetry, the S4 family symmetry and several auxiliary cyclic symmetries, which successfully reproduces the experimentally observed SM fermion mass and mixing pattern. The tiny active neutrino masses are generated through an inverse seesaw mechanism mediated by right-handed Majorana neutrinos. The model is consistent with the SM fermion masses and mixings and successfully accommodates the current Higgs diphoton decay rate constraints as well as the constraints arising from oblique S, T and U parameters and we studied the meson mixing due to flavor changing neutral currents mediated by heavy scalars, finding parameter space consistent with experimental constraints.

Z’ boson mass reach and model discrimination at muon colliders

We study the discrimination power of future multi-TeV muon colliders for a large set of models with extended gauge symmetries and additional neutral gauge bosons (“Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document}-models”). Our study is carried out using a χ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^2$$\\end{document}-analysis of leptonic observables of s-channel scattering in effective Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document}-models. We make use of angular and chiral asymmetries induced in such models to find the discovery reach of a given muon collider setup in terms of the Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z'$$\\end{document} mass and to discriminate between the different scenarios. In this context, we discuss how polarized beams – should they become available at muon colliders – or polarization measurements can help in the discrimination. Our results show that typical muon collider setups which are currently under consideration can give a significantly higher reach compared to existing bounds and projections for high-luminosity LHC.

Trace Conservation Laws in T2/Zm Orbifold Gauge Theories

Abstract Gauge theory compactified on an orbifold is defined by gauge symmetry, matter contents, and boundary conditions (BCs). There are equivalence classes (ECs), each of which consists of physically equivalent BCs. We propose the powerful necessary conditions, trace conservation laws (TCLs), which achieve a sufficient classification of ECs in U(N) and SU(N) gauge theories on T2/Zm orbifolds (m = 2, 3, 4, 6). The TCLs yield the equivalent relations between the diagonal BCs without relying on an explicit form of gauge transformations. The TCLs also show the existence of off-diagonal ECs, which consist only of off-diagonal matrices, on T2/Z4 and T2/Z6. After the sufficient classification, the exact numbers of ECs are obtained.

Unification of symmetries inside neural networks: transformer, feedforward and neural ODE

Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning. This study introduces a novel approach by applying the principles of gauge symmetries, a key concept in physics, to neural network architectures. By regarding model functions as physical observables, we find that parametric redundancies of various machine learning models can be interpreted as gauge symmetries. We mathematically formulate the parametric redundancies in neural ODEs, and find that their gauge symmetries are given by spacetime diffeomorphisms, which play a fundamental role in Einstein’s theory of gravity. Viewing neural ODEs as a continuum version of feedforward neural networks, we show that the parametric redundancies in feedforward neural networks are indeed lifted to diffeomorphisms in neural ODEs. We further extend our analysis to transformer models, finding natural correspondences with neural ODEs and their gauge symmetries. The concept of gauge symmetries sheds light on the complex behavior of deep learning models through physics and provides us with a unifying perspective for analyzing various machine learning architectures.

Holography of broken U(1) symmetry

We examine the Abelian Higgs model in (d + 1)-dimensional anti-de Sitter space with an ultraviolet brane. The gauge symmetry is broken by a bulk Higgs vacuum expectation value triggered on the brane. We propose two separate Goldstone boson equivalence theorems for the boundary and bulk degrees of freedom. We compute the holographic self-energy of the gauge field and show that its spectrum is either a continuum, gapped continuum, or a discretuum as a function of the Higgs bulk mass. When the Higgs has no bulk mass, the AdS isometries are unbroken. We find in that case that the dual CFT has a non-conserved U(1) current whose anomalous dimension is proportional to the square of the Higgs vacuum expectation value. When the Higgs background weakly breaks the AdS isometries, we present an adapted WKB method to solve the gauge field equations. We show that the U(1) current dimension runs logarithmically with the energy scale in accordance with a nearly-marginal U(1)-breaking deformation of the CFT.

Inequivalent light-cone gauge-fixings of strings on AdSn×Sn backgrounds

Light-cone gauge-fixed sigma models on AdSn×Sn backgrounds play an important role in the integrability formulation of the AdS/CFT correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as TT¯, J˜Tτ, JTσ, and Jτ deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to AdS5×S5, compute the different light-cone gauge symmetry algebras, well known to be psu(2|2)⊕2⊕u(1)⊕2 for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models. Published by the American Physical Society 2024

Electrobaryonic axion: hair of neutron stars

Axion-like particles are predicted in many physics scenarios beyond the Standard Model (SM). Their interactions with SM particles may arise from the triangle anomaly of the associated global symmetry, along with other SM global and gauge symmetries, including anomalies with the global baryon number and electromagnetic gauge symmetries. We initiate the phenomenological study of the corresponding “electrobaryonic axion”—a particle that couples with both the baryon chemical potential and the electromagnetic field. Neutron stars, particularly magnetars, possessing high baryon density and strong magnetic fields, can naturally develop a thin axion hair around their surface. In this study, we calculate this phenomenon, considering the effects of neutron star rotation and general relativity. For axion particles lighter than the neutron star rotation frequency, the anomalous interaction can also induce the emission of axion particles from the neutron star. In the light axion regime, this emission can significantly contribute to the neutron star cooling rate.

W_{1+∞} Algebra with a Cosmological Constant and the Celestial Sphere.

It is shown that there exists a simple deformed version of Strominger's infinite-dimensional w_{1+∞} algebra of soft graviton symmetries, which we conjecture to arise in spacetimes with a nonvanishing cosmological constant. The deformed algebra contains a subalgebra generating SO(1,4) or SO(2,3) symmetry groups of dS_{4} or AdS_{4}, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed w_{1+∞} are also discussed.

Quantisation across bubble walls and friction

We quantise from first principles field theories living on the background of a bubble wall in the planar limit with particular focus on the case of spontaneous breaking of gauge symmetry. Using these tools, we compute the average momentum transfer from transition radiation: the soft emission of radiation by an energetic particle passing across the wall, with a particular focus on the longitudinal polarisation of vectors. We find these to be comparable to transverse polarisations in symmetry-breaking transitions with mild super-cooling, and dominant in broken to broken transitions with thin wall. Our results have phenomenological applications for the expansion of bubbles during first order phase transitions. Our general framework allows for the robust calculation of any particle processes of interest in such translation breaking backgrounds.

Interplay between Higgs inflation and dark matter models with dark U(1) gauge symmetry

We investigate dark matter phenomenology and Higgs inflation in a dark U(1)D-extended model. The model features two dark matter candidates, a dark fermion and a dark vector boson. When the fermion dark matter ψ is heavier than the vector dark matter WD, there is an ample parameter space where ψ is dominant over WD. The model can then easily evade the stringent bounds from direct detection experiments, since ψ has no direct coupling to the Standard Model particles. Furthermore, the model can accommodate inflation in three different ways, one along the Standard Model Higgs direction, one along the dark Higgs direction, and one along the combination of the two. Considering the running of the parameters and various observational constraints, we perform a detailed numerical analysis and identify allowed parameter spaces that explain both dark matter and Higgs inflation in a unified manner. We discuss in detail how the imposition of Higgs inflation severely constrains the dark matter parameter space. The existence of the dark Higgs field is found to play a crucial role both in dark matter phenomenology and in generalised Higgs inflation.

Bloch gauge symmetry of the semiconductor Bloch equations [Invited

The semiconductor Bloch equations (SBEs) are a well-established model for optical interactions in condensed matter. In particular, the SBEs in the electromagnetic length gauge preserve the band picture of periodic crystals and thus provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. For materials with broken inversion or time-reversal symmetry, the length gauge SBEs involve complex transition dipole moments (TDMs), which depend on the choice of Bloch gauge. The numerical and conceptual complications resulting from this gauge freedom have impeded interpretation and key applications of HHG, such as the tomographic reconstruction of crystal band structure. We derive gauge invariant SBEs (GI-SBEs) that contain only gauge invariant structural quantities: the absolute value of TDMs, the shift vector, and for more than two bands a triple product of TDM phases. The GI-SBEs provide insight into the physics of HHG in solids with broken inversion symmetry, which we demonstrate in gapped graphene.

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.

Superselection-resolved entanglement in lattice gauge theories: a tensor network approach

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

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.

Coupling Constants as Conserved Charges in Black Hole Thermodynamics.

In a generic theory of gravity coupled to matter fields, the Smarr formula for black holes does not work properly if the contributions of the coupling constants defining the theory are not incorporated. However, these couplings, such as the cosmological constant or the dimensionful parameters that appear in the Lagrangian, are fixed parameters defining the theory, and they cannot be varied. Here, we present a robust method, applicable to any covariant Lagrangian, that upgrades the role of the couplings from being constants in the theory to being free parameters of the solutions. To this end, for each one of the couplings in a theory, a pair of auxiliary scalar and gauge fields is introduced. The couplings are shown to be conserved charges of the global part of the implemented gauge symmetry. Besides, their conjugate chemical potentials are defined as the electric potential of the corresponding gauge fields on the black hole horizon. Using this method, we systematically extend the first law and the Smarr formula by coupling conserved charges and their conjugate potentials. The thermodynamics of a black hole solution in a quadratic gravity theory is given as an example.