Lattice Gerbe Theory

Abstract

We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be $U(1)$, the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group $U(N)\times U(N)$, which gives rise to $U(N)$ Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.

53 pages, 25 figures. Mathematica notebooks for numerically computing Wilson surfaces in 3d and 6d abelian gerbe theory using the heat bath algorithm are attached. References added. Published version

References in corpus (35)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• N=2 dualities
• Open P-Branes
• Covariant Action for a D=11 Five-Brane with the Chiral Field
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Lectures on Special Lagrangian Submanifolds
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Interacting Chiral Gauge Fields in Six Dimensions and Born-Infeld Theory
• M5-branes from gauge theories on the 5-sphere
• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• Deconstructing (2,0) and Little String Theories
• On instantons as Kaluza-Klein modes of M5-branes
• Confining Strings
• Phases of Antisymmetric Tensor Field Theories
• $N^3$-behavior from 5D Yang-Mills theory
• Nonabelian (2,0) Tensor Multiplets and 3-algebras
• On S-duality of 5d super Yang-Mills on S^1
• Instantons on the 5-sphere and M5-branes
• Extrinsic Curvature Dependence of Nielsen-Olesen Strings
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors
• Non-Abelian Tensor Multiplet Equations from Twistor Space
• Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory
• N=4 Supersymmetry on a Space-Time Lattice
• Non-Abelian Tensor Towers and (2,0) Superconformal Theories
• Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space
• Confining String with Topological Term
• Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets
• New superconformal models in six dimensions: Gauge group and representation structure
• Wilson loops in Five-Dimensional Super-Yang-Mills
• Conformal anomaly of Wilson surface observables - a field theoretical computation
• A Nonperturbative Proposal for Nonabelian Tensor Gauge Theory and Dynamical Quantum Yang-Baxter Maps

Cited by in corpus (15)

• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Pinch Point Singularities of Tensor Spin Liquids
• $(k,n)$-fractonic Maxwell theory
• Quantum Information Theory of the Gravitational Anomaly
• Two-dimensional algebra in lattice gauge theory
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Higher Gauge Theory
• ${\mathbb{Z}}_2$ Lattice Gerbe Theory
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• String confinement in 2-form lattice gauge theory
• Higgs Phases and Boundary Criticality