Gauge Symmetry Research Articles

Gauge Symmetry of Magnetic and Electric Two-Potentials with Magnetic Monopoles

Gauge Symmetry of Magnetic and Electric Two-Potentials with Magnetic Monopoles

Faddeev–Jackiw Hamiltonian formulation for general exotic bi-gravity

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants βn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _{n}$$\\end{document} and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds

This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024

SU(3) Gauge Symmetry: An Experimental Review of Diffractive Physics in e+p, p+p, p+A, and A+A Collision Systems

This review focuses on diffractive physics, which involves the long-range interactions of strong nuclear force at high energies described by SU(3) gauge symmetry. It is expected that diffractive processes account for nearly 40% of the total cross-section at LHC energies. These processes consist of soft-scale physics where perturbation theory cannot be applied. Although highly successful and often described as a perfect theory, quantum chromodynamics relies heavily on perturbation theory, a model best suited for hard-scale physics. The study of pomerons could help bridge the soft and hard processes and provide a complete description of the theory of the strong interaction across the full momentum spectrum. Here, we will discuss some of the features of diffractive physics, experimental results from SPS, HERA, and the LHC, and where the field could potentially lead. With the recent publication of the odderon discovery in 2021 by the D0 and TOTEM collaborations and the new horizon of physics that lies ahead with the upcoming Electron-Ion Collider at Brookhaven National Laboratory, interest is seemingly piquing in high energy diffractive physics.

Gauge reduction in covariant field theory

In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the variational principle, we utilize generalized principal connections, a type of Ehresmann connections that are equivariant by the fiberwise action. After obtaining the reduced equations, we give the reconstruction condition and we relate the vertical reduced equation with the Noether theorem. Lastly, we illustrate the theory with several examples, including the classical case (Lagrange–Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories.

The dressing field method for diffeomorphisms: a relational framework

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M) -invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic ‘extended bracket’ for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Frölicher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M) -theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent ( diff(M) ) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M) -invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the ‘dressed’ (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

Deconstructing flavor anomalously

Flavor deconstruction refers to ultraviolet completions of the Standard Model where the gauge group is split into multiple factors under which fermions transform non-universally. We propose a mechanism for charging same-family fermions into different factors of a deconstructed gauge theory in a way that gauge anomalies are avoided. The mechanism relies in the inclusion of a strongly-coupled sector, responsible of both anomaly cancellation and the breaking of the non-universal gauge symmetry. As an application, we propose different flavor deconstructions of the Standard Model that, instead of complete families, uniquely identify specific third-family fermions. All these deconstructions allow for a new physics scale that can be as low as few TeV and provide an excellent starting point for the explanation of the Standard Model flavor hierarchies.

Charges and topology in linearised gravity

Covariant conserved 2-form currents for linearised gravity are constructed by contracting the linearised curvature with conformal Killing-Yano tensors. The corresponding conserved charges were originally introduced by Penrose and have recently been interpreted as the generators of generalised symmetries of the graviton. We introduce an off-shell refinement of these charges and find the relation between these improved Penrose charges and the linearised version of the ADM momentum and angular momentum. If the graviton field is globally well-defined on a background Minkowski space then some of the Penrose charges give the momentum and angular momentum while the remainder vanish. We consider the generalisation in which the graviton has Dirac string singularities or is defined locally in patches, in which case the conventional ADM expressions are not invariant under the graviton gauge symmetry in general. We modify them to render them gauge-invariant and show that the Penrose charges give these modified charges plus certain magnetic gravitational charges. We discuss properties of the Penrose charges, generalise to toroidal Kaluza-Klein compactifications and check our results in a number of examples.

Axion dark matter and additional BSM aspects in an extended 2HDM setup

We illustrate and discuss the phenomenology of a model featuring a two-Higgs doublet sector augmented by two SU(2) singlet scalars. The gauge symmetry group is extended as well with a U(1)Lμ−Lτ component whose spontaneous breaking leads to the gauge boson which has an important effect in the muon (g−2). A global PQ symmetry is introduced upon its breaking; we have the axion particle which is also dark matter (DM) in our work. In particular, we have focused on type-X and type-II 2HDM models and found out that (g−2) cannot be explained only by the scalar sector for type-II 2HDM mainly due to stringent constraint from b→sγ resulted in MH±>800 GeV. For type-II 2HDM, we can have axion coupling with the gluons which generates the axion potential and possible explanation for the strong CP problem. The proposed model accommodates neutrino masses via the type-I seesaw mechanism with an upper bound on the right-handed neutrino mass 1 GeV (1 TeV) for type-II (type-X) 2HDM due to the presence of Planck scale suppressed operators. Moreover, we also have additional scalars which affect the oblique parameters and hence the W-boson mass which leads us to explain the W-boson mass observed at the CDF-II detector. The most stringent constraints on the masses and quartic couplings come from the perturbativity and potential bound from the below conditions which leads to fine-tuning among the parameters in part of the parameter space. Finally, we discuss the possible detection prospects of the axion DM and the additional gauge boson. Published by the American Physical Society 2024

Homological aspects of topological gauge-gravity equivalence

In the works of Achúcarro and Townsend and also by Witten, a duality between three-dimensional Chern–Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous work, we were capable of generalizing Witten’s work to the off-shell cases, as well as to the four-dimensional Yang–Mills theory with de Sitter gauge symmetry. The price we paid is that curvature and torsion must obey some constraints under the action of the interior derivative. These constraints implied on the partial breaking of diffeomorphism invariance. In this work, we first formalize our early results in terms of fiber bundle theory by establishing the formal aspects of the map between a principal bundle (gauge theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism invariance. Then, we study the effect of the constraints on the homology defined by the interior derivative. The main result is the emergence of a non-trivial homology in Riemann–Cartan manifolds.

Topological boundary modes in nonlinear dynamics with chiral symmetry

Particle-hole symmetry and chiral symmetry play a pivotal role in multiple areas of physics, yet they remain unstudied in systems with nonlinear interactions whose nonlinear normal modes do not exhibit U(1) -gauge symmetry. In this work, we establish particle-hole symmetry and chiral symmetry in such systems. Chiral symmetry ensures the quantization of the Berry phase of nonlinear normal modes and categorizes the topological phases of nonlinear dynamics. We show topologically protected static boundary modes in chiral-symmetric nonlinear systems. Furthermore, we demonstrate amplitude-induced nonlinear topological phase transition in chiral-symmetric nonlinear dynamics. Our theoretical framework extends particle-hole and chiral symmetries to nonlinear dynamics, whose nonlinear modes do not necessarily yield U(1) -gauge symmetry.

Gravitational wave signatures of a chiral fermion dark matter model

Theories in which the dark matter (DM) candidate is a fermion transforming chirally under a gauge symmetry are attractive, as the gauge symmetry would protect the DM mass. In such theories, the universe would have undergone a phase transition at early times that generated the DM mass upon spontaneous breaking of the gauge symmetry. In this paper, we explore the gravitational wave signals of a simple such theory based on an SU(2)D dark sector with a dark isospin-3/2 fermion serving as the DM candidate. This is arguably the simplest chiral theory possible. The scalar sector consists of a dark isospin-3 multiple, which breaks the SU(2)D gauge symmetry and also generates the DM mass. We construct the full thermal potential of the model and identify regions of parameter space which lead to detectable gravitational wave signals, arising from a strong first-order SU(2)D phase transition, in various planned space-based interferometers, while also being consistent with dark matter relic abundance. The bulk of the parameter space exhibiting detectable gravitational wave signals in the model also has large WIMP-nucleon scattering cross sections, ℴSI, which could be probed in upcoming direct detection experiments.

Enhancement of the Higgs decay into a Z′ pair in models with U(1)X gauge symmetry

We discuss the Higgs phenomenology in models with a new U(1)X gauge symmetry including the U(1)B−L scenario, where three right-handed neutrinos are inevitably introduced due to the gauge anomaly cancellations. We find that the decay branching ratio of the discovered Higgs boson into a pair of new massive gauge bosons (Z′) can significantly be enhanced in the Dirac neutrino case as compared with the Majorana case for a fixed value of the new gauge coupling and the mass of Z′ under constraints from current experimental data. Because of such an enhancement, the Dirac case can indirectly be discriminated from the Majorana case via the Higgs decay.

Constraints on cosmic-ray boosted dark matter with realistic cross section

Sub-MeV cold dark-matter particles are unable to produce electronic recoil in conventional dark-matter direct detection experiments such as XENONnT and LUX-ZEPLIN above the detector threshold. The mechanism of boosted dark matter comes into picture to constrain the parameter space of such low mass dark matter from direct detection experiments. We consider the effect of the leading components of cosmic rays to boost the cold dark matter, which results in significant improvements on the exclusion limits compared to the existing ones. To present concrete study results, we choose to work on models consisting of a dark-matter particle χ with an additional U(1)' gauge symmetry including the secluded dark photon, U(1)B-L, and U(1)L e-L μ . We find that the energy dependence of the scattering cross section plays a crucial role in improving the constraints. In addition, we systematically estimate the Earth shielding effect on boosted dark matter in losing energy while traveling to the underground detector through the Earth.

Majorana neutrinos and dark matter from anomaly cancellation

We discuss a simple theory for neutrino masses where the total lepton number is a local gauge symmetry spontaneously broken below the multi-TeV scale. In this context, the neutrino masses are generated through the canonical seesaw mechanism and a Majorana dark matter candidate is predicted from anomaly cancellation. We discuss in great detail the dark matter annihilation channels and find out the upper bound on the symmetry-breaking scale using the cosmological bounds on the relic density. Since in this context the dark matter candidate has suppressed couplings to the Standard Model quarks, one can satisfy the direct detection bounds even if the dark matter mass is close to the electroweak scale. This theory predicts a light pseudo-Nambu-Goldstone boson (the Majoron) associated to the mechanism of neutrino mass. We discuss briefly the properties of the Majoron and the impact of the big bang nucleosynthesis bounds. Published by the American Physical Society 2024

Geometrical interpretation of isospin subalgebras in SU(3)

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are [Formula: see text], [Formula: see text] and [Formula: see text] isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.

Asymptotic Weak Gravity Conjecture in M-theory on K3× K3

Abstract The Asymptotic Weak Gravity Conjecture (WGC) has been proposed as a special case of the Tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on a Calabi–Yau threefold (CY3) with finite volume inducing a 5D effective quantum field theory. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalize the obtained 5D Asymptotic WGC to the effective field theory (EFT$_{3D}$) coupled to 3D gravity that descends from M-theory compactified on a Calabi–Yau fourfold with an emphasis on $K3\times K3$. We find that the CY4 has three fibration structures labeled as line Type-$\mathbb {T}^{2}$, surface Type-$\mathbb {S}$, and bulk Type-$\mathbb {V}$. The emergent EFT$_{3D}$ is shown to have 2+2 towers of particle states termed as the BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small BPS}}}$ as well as the non-BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{{\small N-BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{{\small N-BPS}}}$. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the Swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry, are also investigated.

Gauge symmetries and conserved currents in AdS/BCFT

In this paper, we study massless/massive vector and p-form field perturbations in AdS spacetime with an end-of-the-world brane. By imposing Υ(1) preserving Neumann boundary condition on the end-of-the-world brane, we study their spectrum and discuss their implications for dual BCFT operators. When the perturbation is massless, the dual BCFT operator is a conserved current and we show that such an operator indeed satisfies the Υ(1) preserving conformal boundary condition. On the other hand, when the perturbation is massive, in general there exists non-vanishing perpendicular components of the dual BCFT operator, even in the massless limit. We explain this difference between massless and massive perturbations from the point of view of the bulk gauge symmetry, or equivalently from different structure of equations of motion. We also find several brane-tension-independent modes in massless perturbations, and these are understood as boundary-condition-independent modes from the dual BCFT point of view.

Extended doubled structures of algebroids for gauged double field theory

We study an analogue of the Drinfel’d double for algebroids associated with the O(D, D + n) gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a “tripled”, which we call the extended double, rather than the “doubled” structure appearing in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a (2D + n)-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.

Consistency of eight-dimensional supergravities: anomalies, lattices and counterterms

We reexamine the question of quantum consistency of supergravities in eight dimensions. Theories with 16 supercharges suffer from the anomalies under the action of its discrete modular groups. In minimally supersymmetric theory coupled to Yang-Mills multiples of rank l with the moduli space given by SO(2, l)/(U(1) × SO(l)), the existence of a counterterm together with the requirement that its poles and zeros correspond to the gauge symmetry enhancement imposes nontrivial constraints on the lattice. The counterterms needed for anomaly cancellation for all cases, that are believed to lead to consistent theories of quantum gravity (l = 2, 10, 18), are discussed.