Pure gauge theories and spatial periodicity

TL;DR

This paper explores the mathematical equivalence between pure gauge theories in thermal equilibrium and ground state properties of theories with spatially-periodic boundary conditions, revealing topological sectors absent in gauge-invariant formulations.

Contribution

It demonstrates the existence of topological sectors in gauge theories with spatial periodicity that are not present in gauge-invariant formulations, highlighting boundary condition effects.

Findings

Mathematical equivalence of thermal and spatially-periodic gauge theories

Identification of topological sectors absent in gauge-invariant theories

Boundary conditions induce nontrivial topological states

Abstract

Properties of pure gauge theories in thermal equilibrium as calculated via standard functional integral treatments are mathematically identical to ground state properties of a theory with spatially-periodic boundary conditions imposed on the gauge fields. Such a theory has states that have no analog in a theory in which only physical observables associated with gauge-invariant operators are required to be periodic, rather than the gauge fields themselves; these states are in topological sectors that do not exist in the unconstrained theory. The topology arises because the boundary conditions in the functional integral are gauge invariant on a cylinder but not in the unconstrained theory.