Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

TL;DR

This paper investigates how different gauge choices impact the local operator structure and entanglement entropy in 2+1 dimensional lattice gauge theories, proposing new local operators and analyzing their entropy behavior.

Contribution

It introduces a new local operator algebra for gauge fields in 2+1 dimensions and studies the effects of gauge choices and Higgsing on entanglement entropy.

Findings

Entanglement entropy behaves like a scalar field without centers.

Including non-trivial centers makes entropy resemble that of a gauge field.

Higgsing requires deformation of the local operator algebra.

Abstract

In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets. We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions. We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers. We explore also the situation where the gauge field is Higgsed, and construct a local operator algebra that again requires some deformation. This should give us some insight into interpreting the entanglement entropy in generic gauge theories and perhaps also in gravitational theories.