Gauge-invariant Variables and Entanglement Entropy

TL;DR

This paper investigates gauge-invariant variables and their impact on entanglement entropy in various gauge theories, providing new insights into edge modes, contact terms, and topological contributions without relying on the replica method.

Contribution

It introduces a gauge-invariant continuum approach to entanglement entropy, analyzing edge modes and deriving contact terms for both abelian and nonabelian theories.

Findings

Contact term derived from phase space volume measure.

Topological EE contribution calculated for Maxwell-Chern-Simons theory.

Nonabelian EE computed using a gauge-invariant gaussian approximation.

Abstract

The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and nonabelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the nonabelian theory is computed in a gauge-invariant gaussian approximation, which incoprorates the dynamically generated mass gap. A formulation of the contact term for the nonabelian case is also presented.