Abelian Gauge Research Articles

Anomalies of non-invertible symmetries in (3+1)d

Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form gauge theories, with a 0-form permutation symmetry. Gauging the 0-form symmetry gives the 4+1d “inflow” symmetry topological field theory for the non-invertible symmetry. We find a two levels of anomalies: (1) the bulk may fail to have an appropriate set of loop excitations which can condense to trivialize the boundary dynamics, and (2) the “Frobenius-Schur indicator” of the non-invertible symmetry (generalizing the Frobenius-Schur indicator of 1+1d fusion categories) may be incompatible with trivial boundary dynamics. As a consequence we derive conditions for non-invertible symmetries in 3+1d to be compatible with symmetric gapped phases, and invertible gapped phases. Along the way, we see that the defects characterizing \mathbb{Z}_{4}ℤ4 ordinary symmetry host worldvolume theories with time-reversal symmetry \mathsf{T}𝖳 obeying the algebra \mathsf{T}^{2}=C𝖳2=C or \mathsf{T}^{2}=(-1)^{F}C,𝖳2=(−1)FC, with CC a unitary charge conjugation symmetry. We classify the anomalies of this symmetry algebra in 2+1d and further use these ideas to construct 2+1d topological orders with non-invertible time-reversal symmetry that permutes anyons. As a concrete realization of our general discussion, we construct new lattice Hamiltonian models in 3+1d with non-invertible symmetry, and constrain their dynamics.

Sommerfeld enhancement at NLO and the dark matter unitarity bound

We reexamine the consequences of perturbative unitarity on dark matter freeze-out when both Sommerfeld enhancement and bound state formation affect dark matter annihilations. At leading order the annihilation cross section is infrared dominated and the connection between the unitarity bound and the upper bound on the dark matter mass depends only on how the different partial waves are populated. We compute how this picture is modified at next-to-leading order with the goal of assigning a reliable theory uncertainty to the freeze-out predictions. We explicitly compute next-to-leading order corrections in a simple model with Abelian gauge interactions and provide an estimate of the theoretical uncertainty for the thermal masses of heavy electroweak n-plets. Along the way, we clarify the regularization and matching procedure necessary to deal with singular potentials in quantum mechanics with a calculable, relativistic UV completion. Published by the American Physical Society 2024

Light fermion masses in partially deconstructed models

Considering a theory space consisting of a large number of five-dimensional Dirac fermion field theories including background abelian gauge fields, we can construct a theory similar to a continuous six-dimensional theory compactified with two-dimensional manifolds with and without magnetic flux or orbifolds as extra dimensions. This method, called dimensional deconstruction, can be used to construct a model with one-dimensional discrete space, which represents general graph structures. In this paper, we propose the models with two extra dimensions, which resemble two-dimensional tori, cylinders, and rectangular regions, as continuum limits. We also try to build a model that mimics one with the two-dimensional orbifold compactification.

Renormalization flow of nonlinear electrodynamics

We study the renormalization flow of generic actions that depend on the invariants of the field strength tensor of an Abelian gauge field. While the Maxwell action defines a Gaussian fixed point, we search for further non-Gaussian fixed points or rather fixed functions, i.e., globally existing Lagrangians of the invariants. Using standard small-field expansion techniques for the resulting functional flow equation, a large number of fixed points is obtained, which—in analogy to recent findings for a shift-symmetric scalar field—we consider as approximation artifacts. For the construction of a globally existing fixed function, we pay attention to the use of proper initial conditions. Parametrizing the latter by the photon anomalous dimension, both the coefficients of the weak-field expansion are fully determined and those of the large-field expansion can be matched such that a global fixed function can be constructed for magnetic fields. The anomalous dimension also governs the strong-field limit. Our results provide evidence for the existence of a continuum of non-Gaussian fixed points parametrized by a small positive anomalous dimension below a critical value. We discuss the implications of this result within various scenarios with and without additional matter. For the strong-field limit of the 1PI QED effective action, where the anomalous dimension is determined by electronic fluctuations, our result suggests the existence of a singularity free strong-field limit, circumventing the standard conclusions connected to the perturbative Landau pole. Published by the American Physical Society 2024

Anomaly inflow, dualities, and quantum simulation of Abelian lattice gauge theories induced by measurements

Previous work [] has demonstrated that quantum simulation of Abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their noninvertibility are also presented. Published by the American Physical Society 2024

Spin Exchange-Enabled Quantum Simulator for Large-Scale Non-Abelian Gauge Theories

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU(N) and U(N) LGTs with dynamical matter in d+1D, enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2+1DSU(2) and U(2) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024

Gauge-invariant quantum fields

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant description of the Higgs mode via a propagating gauge-invariant field. The renormalization of the model is studied in the Algebraic Renormalization approach. The decomposition of Slavnov–Taylor identities into separately invariant sectors is analyzed. We also comment on some non-renormalizable extensions of the model whose 1-PI Green’s functions are the flows of certain differential equations of the homogeneous Euler type, exactly resumming the dependence on a certain set of dim. 6 and dim. 8 derivative operators. The latter are identified uniquely by the condition that they span the mass and kinetic terms in the gauge-invariant dynamical fields. The construction can be extended to non-Abelian gauge groups.

Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma – defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD – remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.

Dijet spectrum in nonlocal and asymptotically nonlocal theories

Asymptotically nonlocal field theories approximate ghost-free nonlocal theories at low energies, yet are theories of finite order in the number of derivatives. These theories have an emergent nonlocal scale that regulates loop diagrams and can provide a solution to the hierarchy problem. Asymptotic nonlocality has been studied previously in scalar theories, Abelian and non-Abelian gauge theories with complex scalars, and linearized gravity. Here we extend that work by considering an asymptotically nonlocal generalization of QCD, which can be used for realistic phenomenological investigations. In particular, we derive Feynman rules relevant for the study of the production of dijets at hadron colliders and compute the parton-level cross sections at leading order. We use these to determine a bound on the scale of new physics from Large Hadron Collider data, both for a typical choice of model parameters, and in the nonlocal limit. Published by the American Physical Society 2024

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two ‘hydrodynamic’ Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form ℤ2 symmetry of the bosonic theory and its gauging, which originates the fermion number (−1)F, the spin sectors and the time reversal symmetry obeying T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}2 = (−1)F. These results are detailed for the effective action and the partition function on the geometry S2 × S1.

Flat space spinning massive amplitudes from momentum space CFT

We discuss the flat space limit of AdS using the momentum space representation of CFT correlators. The flat space limit involves sending the AdS radius and the dimensions of operators dual to massive fields to infinity while also scaling appropriately the sources of the dual operators. In this limit, d-dimensional CFT correlators become (d + 1)-dimensional scattering amplitudes. We exemplify our discussion with the computation of the flat-space limit of the CFT 3-point function of a conserved current, a non-conserved charged vector operator and its conjugate. The flat-space limit should yield the scattering amplitude of an Abelian gauge field with two massive vector fields. This scattering amplitude computes the electromagnetic form factors of the electromagnetic current in a spin-1 state, and these form factors encode the electromagnetic properties of the massive vector field (charge, magnetic moment and quadruple moment). In terms of the CFT, the flat-space limit amounts to zooming in the infrared region of the triple-K integrals that determine the 3-point function, while also scaling to infinity the order of (some of) the Bessel functions that feature in the triple-K integrals. In this limit the triple-K integral becomes proportional to the energy-preserving delta function, and the flat space limit correctly yields the corresponding flat space scattering amplitude in complete detail.

What can abelian gauge theories teach us about kinematic algebras?

The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

Bootstrapping the Abelian lattice gauge theories

We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ Lmax to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large Lmax = 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10−8 or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ2 and U(1) lattice gauge theories with Lmax = 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories.

De Sitter at all loops: the story of the Schwinger model

We consider the two-dimensional Schwinger model of a massless charged fermion coupled to an Abelian gauge field on a fixed de Sitter background. The theory admits an exact solution, first examined by Jayewardena, and can be analyzed efficiently using Euclidean methods. We calculate fully non-perturbative, gauge-invariant correlation functions of the electric field as well as the fermion and analyze these correlators in the late-time limit. We compare these results with the perturbative picture, for example by verifying that the one-loop contribution to the fermion two-point function, as predicted from the exact solution, matches the direct computation of the one-loop Feynman diagram. We demonstrate many features endemic of quantum field theory in de Sitter space, including the appearance of late-time logarithms, their resummation to de Sitter invariant expressions, and Boltzmann suppressed non-perturbative phenomena, with surprising late-time features.

Gravitational axiverse spectroscopy: seeing the forest for the axions

We consider inflationary models with multiple spectator axions coupled to dark gauge sectors via Chern-Simons (CS) terms. The energy injection into Abelian gauge fields from the axions engenders a multi-peak profile for scalar and tensor spectra. We highlight the constraining power of CMB spectral distortions on the scalar signal and discuss the conditions under which spectator sectors can account for the recently observed stochastic gravitational wave (GW) background in the nHz range. Given the tantalizing prospect of a multi-peak “GW forest” spanning several decades in frequency, we elaborate on possible ultraviolet origins of the spectator models from Type IIB orientifolds. String compactifications generically produce a multitude of axions, the “Axiverse”, from dimensional reduction of p-form gauge fields. The CS coupling of such axions to dark gauge fields in the worldvolume theory of D7-branes can be tuned via multiple brane wrappings and/or quantized gauge field strengths. If string axions coupled to Abelian gauge fields undergo slow-roll during inflation, they produce GW signals with peaked frequency distribution whose magnitude depends on the details of the compactification. We discuss the restrictions on spectator models from consistency and control requirements of the string compactification and thereby motivate models that may live in the string landscape as opposed to the swampland.

Dimensional reduction gauge and effective dimensional reduction in four-dimensional Yang-Mills theory

Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of “dimensional reduction (DR) gauge” defined so as to minimize RDR≡∫d4sTr[Ax2(s)+Ay2(s)], which has a residual gauge symmetry for the gauge function Ω(t,z) like 2D QCD on the t−z plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at β=6.0. The amplitude of Ax(s) and Ay(s) are found to be strongly suppressed in the DR gauge. We consider “tz-projection” of Ax,y(s)→0 for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the tz-projection in the DR gauge, the interquark potential is not changed, and At(s) and Az(s) play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation ⟨TrA⊥(s)A⊥(s+ra⊥)⟩(⊥=x,y) and estimate the spatial mass of A⊥(s)(⊥=x,y) as M≃1.7 GeV. It is conjectured that this large mass makes A⊥(s) inactive and realizes the dominance of At(s) and Az(s) in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as exp(−mr) with m≃0.6 GeV. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of g2D=gm. Published by the American Physical Society 2024

Chern-Simons gravity and PT symmetry

This paper considers the possibility that, starting from a relativistic Hermitian quantum field theory in the ultraviolet (UV) regime, and applying a nonperturbative renormalization-group (RG) flow, we arrive at a situation where there are infrared (IR) singularities in the RG flow of couplings. The latter can be resolved by assuming that the theory can have a phase described by a related non-Hermitian PT-symmetric modification in the IR. The UV-to-IR (Hermitian-to-PT-symmetric) transition can occur in a single renormalization-group flow of the pertinent couplings, as demonstrated in concrete examples. When embedded in a gravitational setting such a transition can lead to a repulsive gravity phase. If there is a RG flow to a repulsive PT -symmetric gravity, then this would be an alternative to dark energy. The discussion here is presented in the context of a string-inspired Chern-Simons gravitational effective action, which involves a pseudoscalar (axionlike) field coupled to Abelian gauge fields and gravity; it may also hold more generally in gravity with torsion. The validity of such a scenario in realistic theories might alleviate the need for de Sitter phases in the current epoch of cosmological evolution, thus avoiding their associated conceptual and technical complications. Published by the American Physical Society 2024

A 3D field-theoretic example for Hodge theory

We focus on the continuous symmetry transformations for the three (2 + 1)-dimensional (3D) system of a combination of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We establish that this combined system is a tractable field-theoretic model of Hodge theory. The symmetry operators of our present system provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. Our present investigation is important in the sense that, for the first time, we are able to establish an odd dimensional (i.e., D = 3) field-theoretic system to be an example for Hodge theory (besides earlier works on a few interesting (0 + 1)-dimensional (1D) toy models as well as a set of well-known SUSY quantum mechanical systems of physical interest). For the sake of brevity, we have purposely not taken into account the 3D Chern-Simon term for the Abelian 1-form gauge field in our theory which allows the mass as well as the gauge invariance to co-exist together.

Phase transitions and composite order in U(1)N lattice London models

The phase diagrams and the nature of the phase transitions in multicomponent gauge theories with an Abelian gauge field are important topics with various physical applications. While an early renormalization-group-based study indicated that the direct transition from a fully ordered to a fully disordered state is continuous for N=1 and N>183, recently it was demonstrated that the transition is discontinuous for N=2. We quantitatively study the dependence on N of the degree of discontinuity of this transition. Our results suggest that the transition is discontinuous at least up to N=7. Furthermore, we demonstrate that, at increased coupling strength, the phase transitions of the neutral and charged sectors of the model split, which for N>2 yields a new phase with composite order. The transition from the composite-order phase to the fully disordered phase is then also discontinuous, at least for N=3 and N=4. Via a duality argument, this indicates that van der Waals–type interaction between directed loops may be responsible for the discontinuous phase transitions in these models. Published by the American Physical Society 2024

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.