Gauge Theory Research Articles

Relaxation of first-class constraints and the quantization of gauge theories: From “matter without matter” to the reappearance of time in quantum gravity

We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock–Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls and generalizes the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research.

Gauge Theory Without Principal Fiber Bundles

Abstract In general relativity, the strong equivalence principle is underpinned by a geometrical account of fields on spacetime, by which all fields and bodies probe the same geometry. This geometric account implies that the parallel transport of all spacetime tensors and spinors is dictated by a single affine connection. No similar account of gauge theory is put forward by standard textbooks, which use principal bundles to coordinate the parallel transport of different, interacting particles. Nonetheless, here I argue that gauge theory does afford such a geometric account, obviating the need for principal bundles.

Hunting 3d N\\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} = 1 SQED in the ϵ-expansion

It was recently shown that 3dN\\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} = 1 supersymmetric Wess-Zumino models can be studied in the ϵ-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider U(1) gauge theories with Ng neutral Majorana fermions χa, Nf charge-1 bosons ϕi and Nf × Ng charge-1 Dirac fermions ψia in the d = 4 − 2ϵ expansion. Analytically continuing to Ng = 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} schematically matches the Lagrangian and matter content of 3dN\\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} = 1 SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of χa up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small Nf, at large Nf the observables approach the expected values at a SUSY fixed point. This may allow for checks of 3dN\\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} = 1 IR dualities between gauge theories.

Bosonic quantum integrable systems and gauge theories

Bosonic quantum integrable systems and gauge theories

Proof of An AGT conjecture at β = 1

AGT conjecture reveals a connection between 4D N\\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 gauge theory and 2D conformal field theory. Though some special instances have been proven, others remain elusive and the attempts on its full proof never stop. When the Ω background parameters satisfy −ϵ1/ϵ2 ≡ β = 1, the story can be simplified a bit. A proof of the correspondence in the case of A1 gauge group was given in 2010 by Mironov et al., while the An extension is verified by Matsuo and Zhang in 2011, with an assumption on the Selberg integral of n + 1 Schur polynomials. Then in 2020, Albion et al. obtained the rigorous result of this formula. In this paper, we show that the conjecture on the Selberg integral of Schur polynomials is formally equivalent to their result, after applying a more complicated complex contour, thus leading to the proof of the An case at β = 1. To perform a double check, we also directly start from this formula, and manage to show the identification between the two sides of AGT correspondence.

Algorithms for numerically stable scattering amplitudes

The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double-precision arithmetic and reaches higher precision than a naive quadruple-precision implementation at smaller computational cost. The method is based on physics-driven modifications to propagators, vertices, and external polarizations. Published by the American Physical Society 2024

Decomposition squared

In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of parallel one-dimensional objects (such as Wilson lines) and dimensional reductions to two dimensions do decompose, sometimes in two independent ways. We apply this to extend conjectures for quantum K theory rings of gerbes (realized by three-dimensional gauge theories with one-form symmetries) via both orbifold partition functions and gauged linear sigma models.

Cold-Atom Particle Collider

A major objective of the strong ongoing drive to realize quantum simulators of gauge theories is achieving the capability to probe collider-relevant physics on them. In this regard, a highly pertinent and sought-after application is the controlled collisions of elementary and composite particles, as well as the scattering processes in their wake. Here, we propose particle-collision experiments in a cold-atom quantum simulator for a 1+1D (one spatial and one temporal dimension) U(1) lattice gauge theory with a tunable topological θ term, where we demonstrate an experimentally feasible protocol to impart momenta to elementary (anti)particles and their meson composites. We numerically benchmark the collisions of moving wave packets for both elementary and composite particles, uncovering a plethora of rich phenomena, such as oscillatory string dynamics in the wake of elementary (anti)particle collisions due to confinement. We also probe string inversion and entropy production processes across Coleman’s phase transition through far-from-equilibrium quenches. We further demonstrate how collisions of composite particles unveil their internal structure. Our work paves the way towards the experimental investigation of collision dynamics in state-of-the-art quantum simulators of gauge theories, and sets the stage for microscopic understanding of collider-relevant physics in these platforms. Published by the American Physical Society 2024

Digital Quantum Simulation of a (1+1)D SU(2) Lattice Gauge Theory with Ion Qudits

We present a quantum simulation strategy for a (1+1)-dimensional SU(2) non-Abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion-qudit quantum processor, as recently experimentally realized [Nat. Phys. 18, 1053 (2022)]. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss’s law. We discuss the experimental feasibility of generalized Mølmer-Sørensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically relevant properties specific to non-Abelian field theories, such as baryon excitations. Published by the American Physical Society 2024

Basic curvature and the Atiyah cocycle in gauge theory

Abstract Motivated from target space covariant formulations of topological sigma models and from a graded-geometric approach to higher gauge theory, we study connections on Lie and Courant algebroids and on their description as differential graded (dg) manifolds. We revisit the notion of basic curvature for a connection on a Lie algebroid, which measures its compatibility with the Lie bracket and it appears in the BV-BRST differential of 2D gauge theories such as (twisted) Poisson and Dirac sigma models. We define a basic curvature tensor for connections on Courant algebroids and we show that in the description of a Courant algebroid as a QP2 manifold it appears naturally as part of the homological vector field together with the Gualtieri torsion of an induced generalised connection. Furthermore, we consider connections on dg manifolds and revisit the structure of gauge transformations in the graded-geometric approach to higher gauge theories from a manifestly covariant perspective. We argue that it is governed by the brackets of a Kapranov L$_{\infty}[1]$ algebra, whose binary bracket is given by the Atiyah cocycle that measures the compatibility of the connection with the homological vector field. We also revisit some aspects of the derived bracket construction and show how to extend it to connections and tensors.

Preserving quantum information in f(Q) non-metric gravity cosmology

The effects of cosmological expansion on quantum bosonic states are investigated, using quantum information theory. In particular, a generic Bogoliubov transformation of bosonic field modes is considered and the state change on a single mode is regarded as the effect of a quantum channel. Properties and capacities of this channel are thus explored in the framework of f(Q) non-metric gravity. The reason is that non-metric gravity can be considered under the standard of gauge theories with all the advantages of such a formulation. As immediate result, we obtain that the information on a single-mode state appears better preserved, whenever the number of particles produced by the cosmological expansion is small. Specifically, we investigate a power law f(Q) model, leaving unaltered the effective gravitational coupling, and minimise the corresponding particle production. We thus show how to optimise the preservation of classical and quantum information, stored in bosonic mode states in the remote past. Finally, we compare our findings with those obtained in General Relativity.

Embedding space approach to Jackiw-Teitelboim gravity

We present a coordinate-free background space construction of Euclidean Jackiw-Teitelboim gravity. It is written as a gauge theory obtained from the Killing vectors and conformal Killing vectors of a hyperboloid embedded in a three-dimensional background. A novel feature of the gauge theory is that vanishing field strength does not necessarily imply that the gauge potentials (written in the embedding space) are pure gauges, not even locally. On the other hand, the projection of the potentials along the hyperboloid are pure gauges, as is the case in the standard approach. As is usual, metric tensors are dynamically generated from the classical solutions of the theory, which here do not rely on coordinate charts on the two-dimensional surface. We find a special class of solutions whereby the derived metric tensor on the surface is the induced metric from the background space. The gauge theory construction given here has a natural generalization to a noncommutative space, which does not require the use of coordinates, symbols, or a star product. Published by the American Physical Society 2024

Global aspects of 3-form gauge theory: implications for axion-Yang-Mills systems

We investigate the proposition that axion-Yang-Mills systems are characterized by a 3-form gauge theory in the deep infrared regime. This hypothesis is rigorously examined by initially developing a systematic framework for analyzing 3-form gauge theory coupled to an axion, specifically focusing on its global properties. The theory consists of a BF term deformed by marginal and irrelevant operators and describes a network of vacua separated by domain walls converging at the junction of an axion string. It encompasses 0- and 3-form spontaneously broken global symmetries. Utilizing this framework, in conjunction with effective field theory techniques and ’t Hooft anomaly-matching conditions, we argue that the 3-form gauge theory faithfully captures the infrared physics of the axion-Yang-Mills system. The ultraviolet theory is an SU(N) Yang-Mills theory endowed with a massless Dirac fermion coupled to a complex scalar and is characterized by chiral and genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} 1-form center symmetries, with a mixed anomaly between them. It features two scales: the vev of the complex scalar, v, and the strong-coupling scale, Λ, with Λ ≪ v. Below v, the fermion decouples and a U(1)(2) 2-form winding symmetry emerge, while the 1-form symmetry is enhanced to ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document}. As we flow below Λ, matching the mixed anomaly necessitates introducing a dynamical 3-form gauge field of U(1)(2), which appears as the incarnation of a long-range tail of the color field. The infrared theory possesses spontaneously broken chiral and emergent 3-form global symmetries. It passes several checks, among which: it displays the expected restructuring in the hadronic sector upon transition between the vacua, and it is consistent under the gauging of the genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} ⊂ ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document} symmetry.

Deep learning lattice gauge theories

Deep learning lattice gauge theories

Digitization and subduction of SU(N) gauge theories

The simulation of lattice gauge theories on quantum computers necessitates digitizing gauge fields. One approach involves substituting the continuous gauge group with a discrete subgroup, but the implications of this approximation still need to be clarified. To gain insights, we investigate the subduction of SU(2) and SU(3) to discrete crystal-like subgroups. Using classical lattice calculations, we show that subduction offers valuable information based on subduced direct sums, helping us identify additional terms to incorporate into the lattice action that can mitigate the effects of digitization. Furthermore, we compute the static potentials of all irreducible representations of Σ(360×3) at a fixed lattice spacing. Our results reveal a percent-level agreement with the Casimir scaling of SU(3) for irreducible representations that subduce to a single Σ(360×3) irreducible representation. This provides a diagnostic measure of approximation quality, as some irreducible representations closely match the expected results while others exhibit significant deviations. Published by the American Physical Society 2024

Levin-Wen is a Gauge Theory: Entanglement from Topology

We show that the Levin-Wen model of a unitary fusion category C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document} is a gauge theory with gauge symmetry given by the tube algebra Tube(C)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Tube}}({\\mathcal {C}})$$\\end{document}. In particular, we define a model corresponding to a Tube(C)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {Tube}}({\\mathcal {C}})$$\\end{document} symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case C=Hilb(G,ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}=\ extsf{Hilb}(G,\\omega )$$\\end{document}, we show how our procedure reduces to the twisted gauging of a trival G-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibbonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter.

Comments on Global Symmetries and Anomalies of 5d SCFTs

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed ’t Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional N=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=4$$\\end{document} SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries.

Time-reversal anomalies of QCD3 and QED3

Anomalies of global symmetry provide powerful tool to constrain the dynamics of quantum systems, such as anomaly matching in the renormalization group flow and obstruction to symmetric mass generation. In this note we compute the anomalies in 2+1d time-reversal symmetric gauge theories with massless fermions in the fundamental and rank-two tensor representations, where the gauge groups are SU(N), SO(N), Sp(N), U(1). The fermion parity is part of the gauge group and the theories are bosonic. The time-reversal symmetry satisfies T2 = 1 or T2 = M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} where M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} is an internal magnetic symmetry. We show that some of the bosonic gauge theories have time-reversal anomaly with c− ≠ 0 mod 8 that is absent in fermionic systems. The anomalies of the gauge theories can be nontrivial even when the number of Majorana fermions is a multiple of 16 and ν = 0.

Meson spectroscopy from spectral densities in lattice gauge theories

Spectral densities encode nonperturbative information that enters the calculation of a plethora of physical observables in strongly coupled field theories. Phenomenological applications encompass aspects of standard-model hadronic physics, observable at current colliders, as well as correlation functions characterizing new physics proposals, testable in future experiments. By making use of numerical data produced in a Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group, we perform a systematic study to demonstrate the effectiveness of recent technological progress in the reconstruction of spectral densities.To this purpose, we write and test new software packages that use energy-smeared spectral densities to analyze the mass spectrum of mesons. We assess the effectiveness of different smearing kernels and optimize the smearing parameters to the characteristics of available lattice ensembles. For concreteness, we analyze the Sp(4) lattice gauge theory with matter transforming in an admixture of fundamental and 2-index antisymmetric representations of the gauge group. We generate new ensembles for the theory in consideration, with lattices that have a longer extent in the time direction with respect to the spatial ones. We run our tests on these ensembles, obtaining new results about the spectrum of light mesons and their excitations. We make available our algorithm and software for the extraction of spectral densities, that can be applied to theories with other gauge groups, including the theory of strong interactions (QCD) governing hadronic physics in the standard model. Published by the American Physical Society 2024

Magic of discrete Lattice Gauge theories

Simulation of quantum field theories and fundamental interactions is one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for [Formula: see text] LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.