Gauge Theory Models Research Articles

Presymplectic minimal models of local gauge theories

Presymplectic minimal models of local gauge theories

Gauge theory on ρ-Minkowski space-time

We construct a gauge theory model on the 4-dimensional ρ-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of ρ-deformed translations, a Hopf subalgebra of the ρ-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the ρ-Minkowski space-time. The gauge theory model is left invariant under the action of the ρ-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

We present a gauge and Lorentz invariant effective field theory model for the interaction of a charged scalar matter field with a magnetic monopole source, described by an external magnetic current. The quantum fluctuations of the monopole field are described effectively by a strongly coupled “dual” Ud(1) gauge field, which is independent of the electromagnetic Uem(1) gauge field. The effective interactions of the charged matter with the monopole source are described by a gauge invariant mixed Chern-Simons-like (Pontryagin-density) term between the two U(1) gauge fields. The latter interaction coupling is left free, and a lattice study of the system is performed with the aim of determining the phase structure of this effective theory. Our study shows that, in the spontaneously broken-symmetry phase, the monopole source triggers, via the mixed Chern-Simons term, which is nontrivial in its presence, the generation of a dynamical singular configuration (magnetic-monopolelike) for the respective gauge fields. The scalar field also behaves in the broken phase in a way similar to that of the scalar sector of the ’t Hooft-Polyakov monopole. Moreover, we show that the modest size of the lattices involved does not have significant effects on the main conclusions of our analysis. Published by the American Physical Society 2024

Excitations in the higher-lattice gauge theory model for topological phases. III. The (3+1)-dimensional case

In this, the third paper in our series describing the excitations of the higher-lattice gauge theory model for topological phases, we will examine the (3+1)-dimensional case in detail. We will explicitly construct the ribbon and membrane operators which create the topological excitations, and use these creation operators to find the pattern of condensation and confinement. We also use these operators to find the braiding relations of the excitations, and to construct charge measurement operators which project to states of definite topological charge. Published by the American Physical Society 2024

Excitations in the higher-lattice gauge theory model for topological phases. I. Overview

Excitations in the higher-lattice gauge theory model for topological phases. I. Overview

Quantum optimization within lattice gauge theory model on a quantum simulator

Simulating lattice gauge theory (LGT) Hamiltonian and its nontrivial states by programmable quantum devices has attracted numerous attention in recent years. Rydberg atom arrays constitute one of the most rapidly developing arenas for quantum simulation and quantum computing. The {{mathbb{Z}}}_{2} LGT and topological order has been realized in experiments while the U(1) LGT is being worked hard on the way. States of LGT have local constraints and are fragmented into several winding sectors with topological protection. It is therefore difficult to reach the ground state in target sector for experiments, and it is also an important task for quantum topological memory. Here, we propose a protocol of sweeping quantum annealing (SQA) for searching the ground state among topological sectors. With the quantum Monte Carlo method, we show that this SQA has linear time complexity of size with applications to the antiferromagnetic transverse field Ising model, which has emergent U(1) gauge fields. This SQA protocol can be realized easily on quantum simulation platforms such as Rydberg array and D-wave annealer. We expect this approach would provide an efficient recipe for resolving the topological hindrances in quantum optimization and the preparation of quantum topological state.

Holographic light dilaton at the conformal edge

We study a simple holographic model for gauge theories near the conformal edge to show that the dilaton can be parametrically lighter than any other composite states. The masses of all composite states, except the Nambu-Goldstone bosons like dilaton, are bounded by the infrared scale or the dynamical mass. The parametric dependence of the dilaton mass is controlled by the closeness of the anomalous dimension of the quark bilinear, that breaks spontaneously the scale symmetry, to the conformality. We also show in the holographic dual that under certain assumptions, the dilaton saturates at low energy the anomalous Ward identity for the dilatation currents.

Aspects of supergroup gauge theory

In this paper, provide a survey of recent studies of supergroup gauge theory. We first discuss the supermatrix model as a zero-dimensional toy model of supergroup gauge theory and its geometric and algebraic characterization. We then focus on four-dimensional Yang–Mills theory with supergroup gauge symmetry and explore its nonperturbative properties, including instanton calculus, Seiberg–Witten geometry, Bethe/gauge correspondence, and its realization with intersecting defects.

Spectrum of large N glueballs: holography vs lattice

Recently there has been a notable progress in the study of glueball states in lattice gauge theories, in particular extrapolating their spectrum to the limit of large number of colors N. In this note we compare the large N lattice results with the holographic predictions, focusing on the Klebanov-Strassler model, which describes a gauge theory with mathcal{N} = 1 supersymmetry. We note that glueball spectrum demonstrates approximate universality across a range of gauge theory models. Because of this universality the holographic models can give reliable predictions for the spectrum of pure SU(N) Yang-Mills theories with and without supersymmetry. This is especially important for the supersymmetric theories, for which no firm lattice predictions exist yet, and the holographic models remain the most tractable approach. For SU(N) theories with large N the lattice non-supersymmetric and holographic supersymmetric predictions for the mass ratios of the lightest states in various sectors agree up to 5–8%, supporting the proposed universality. In particular, both lattice and holography give predictions for the 2++ and 1−− mass ratio, consistent with the known constraints on the pomeron and odderon Regge trajectories.

Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate

Topological gauge theories provide powerful effective descriptions of certain strongly correlated systems, a prime example being the Chern-Simons gauge theory of fractional quantum Hall states. Engineering topological gauge theories in controlled quantum systems is of both conceptual and practical importance, as it would provide access to systems with exotic excitations such as anyons without the need for strong correlations. Here, we discuss a scheme to engineer the chiral BF theory, a minimal model of a topological gauge theory corresponding to a one-dimensional reduction of the Chern-Simons theory, with ultracold atoms. Using the local conservation laws of the theory, we encode its quantum Hamitonian into an ultracold quantum gas with chiral interactions. Building on a seminal proposal by Edmonds et al. (Phys. Rev. Lett. 110, 085301 (2013)), we show how to implement it in a Raman-coupled Bose-Einstein condensate with imbalanced scattering lengths, as we have recently realized experimentally (Fr\"olian et al., Nature 608, 293 (2022)). We discuss the properties of the chiral condensate from a gauge theory perspective, and assess the validity of the effective quantum description for accessible experimental parameters via numerical simulations. Our approach lays the foundation for realizing topological gauge theories in higher dimensions with Bose-Einstein condensates.

Some Classical Models of Particles and Quantum Gauge Theories

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.

Cosmology of a Polynomial Model for de Sitter Gauge Theory Sourced by a Fluid

In the de Sitter gauge theory (DGT), the fundamental variables are the de Sitter (dS) connection and the gravitational Higgs/Goldstone field ξA, where A is a 5 dimensional index. Previously, a model for DGT was analyzed, which generalizes the MacDowell–Mansouri gravity to have a variable cosmological constant, Λ=3/l2, where l is related to ξA by ξAξA=l2. It was shown that the model sourced by a perfect fluid does not support a radiation epoch and the accelerated expansion of the parity invariant universe. In this paper, I consider a similar model, namely, the Stelle–West gravity, and couple it to a modified perfect fluid, such that the total Lagrangian 4-form is polynomial in the gravitational variables. The Lagrangian of the modified fluid has a nontrivial variational derivative with respect to l, and as a result, the problems encountered in the previous study no longer appear. Moreover, to explore the elegance of the general theory, as well as to write down the basic framework, I perform the Lagrange–Noether analysis for DGT sourced by a matter field, yielding the field equations and the identities with respect to the symmetries of the system. The resulted formula are dS covariant and do not rely on the existence of the metric field.

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a \mathrm{U}(1)U(1) quantum link lattice gauge theory where the gauge fields, represented by spin-\frac{1}{2}12 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1)(2+1)-d. This model allows us to smoothly tune between the \mathrm{U}(1)U(1) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

Phase structure of self-dual lattice gauge theories in 4d

We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their ’t Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of ℤ4 by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.

A First-Quantized Model for Unparticles and Gauge Theories around Conformal Window

We first quantize an action proposed by Casalbuoni and Gomis in 2014 that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in terms of an effective string tension σ. The quantized model is confining when σ≠0 and its mass spectrum shows Regge trajectories. We propose a tensionless limit in which highly excited confined states reduce to (gapped) unparticles. Moreover, the low-lying confined bound states become massless in the latter limit as a sign of conformal symmetry restoration and the ratio between their masses and σ stays constant. The originality of our approach is that it applies to both confining and conformal phases via an effective interacting model.

Dynamics of a lattice 2-group gauge theory model

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

Holographic Coulomb branch solitons, quasinormal modes, and black holes

Four-dimensional mathcal{N} = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

An mathcal{N} = 1 Lagrangian for the rank 1 E6 superconformal theory

We propose that a certain 4d mathcal{N} = 1 SU(4) gauge theory flows in the IR to the rank 1 mathcal{N} = 2 strongly coupled SCFT with E6 global symmetry and 25 free chiral fields. This proposal is tested by comparing various RG invariant quantities, notably, anomalies and the superconformal index. We discuss the generalization to mathcal{N} = 1 SU(2n + 2) gauge theory models flowing in the IR to the R(2,2n+1) family of strongly coupled SCFTs plus free fields.

Taming defects in mathcal{N} = 4 super-Yang-Mills

We study correlation functions involving extended defect operators in the four- dimensional mathcal{N} = 4 super-Yang-Mills (SYM). The main tool is supersymmetric localization with respect to the supercharge \U0001d4ac introduced in [1] which computes observables in the \U0001d4ac- cohomology. We classify general defects of different codimensions in the mathcal{N} = 4 SYM that belong to the \U0001d4ac-cohomology, which form 1 -BPS defect networks. By performing the \U0001d4ac- localization of the mathcal{N} = 4 SYM on the four-dimensional hemisphere, we discover a novel defect-Yang-Mills (dYM) theory on a submanifold given by the two-dimensional hemisphere and described by (constrained) two-dimensional Yang-Mills coupled to topological quantum mechanics on the boundary circle. This also generalizes to interface defects in mathcal{N} = 4 SYM by the folding trick. We provide explicit dictionary between defect observables in the SYM and those in the dYM, which enables extraction of general frac{1}{16} -BPS defect network observables of the SYM from two-dimensional gauge theory and matrix model techniques. Applied to the D5 brane interface in the SU(N ) SYM, we explicitly determine a set of defect correlation functions in the large N limit and obtain precise matching with strong coupling results from IIB supergravity on AdS5× S5.

Higher lattices, discrete two-dimensional holonomy and topological phases in (3 + 1)D with higher gauge symmetry

Higher gauge theory is a higher order version of gauge theory that makes possible the definition of 2-dimensional holonomy along surfaces embedded in a manifold where a gauge 2-connection is present. In this paper, we study Hamiltonian models for discrete higher gauge theory on a lattice decomposition of a manifold. We show that a construction for higher lattice gauge theory is well-defined, including in particular a Hamiltonian for topological phases of matter in [Formula: see text] dimensions. Our construction builds upon the Kitaev quantum double model, replacing the finite gauge connection with a finite gauge 2-group 2-connection. Our Hamiltonian higher lattice gauge theory model is defined on spatial manifolds of arbitrary dimension presented by slightly combinatorialized CW-decompositions (2-lattice decompositions), whose 1-cells and 2-cells carry discrete 1-dimensional and 2-dimensional holonomy data. We prove that the ground-state degeneracy of Hamiltonian higher lattice gauge theory is a topological invariant of manifolds, coinciding with the number of homotopy classes of maps from the manifold to the classifying space of the underlying gauge 2-group. The operators of our Hamiltonian model are closely related to discrete 2-dimensional holonomy operators for discretized 2-connections on manifolds with a 2-lattice decomposition. We therefore address the definition of discrete 2-dimensional holonomy for surfaces embedded in 2-lattices. Several results concerning the well-definedness of discrete 2-dimensional holonomy, and its construction in a combinatorial and algebraic topological setting are presented.