Entanglement entropy in d+1 SU(N) gauge theory

TL;DR

This paper investigates the behavior of entanglement entropy in SU(N) gauge theories across different dimensions, revealing a phase transition-like change in the entropy's form in higher dimensions.

Contribution

It provides an exact analysis for 1+1 dimensions and employs Migdal-Kadanoff approximation for higher dimensions to identify a non-analytical transition in entanglement entropy.

Findings

Exact solution for 1+1 gauge theory shows trivial behavior.

Identification of a non-analytical change in entanglement entropy in higher dimensions.

Transition linked to nontrivial RG flow of partition function coefficients.

Abstract

We consider the entanglement entropy for a sub-system in d+1 dimensional SU(N) lattice gauge theory. The 1+1 gauge theory is treated exactly and shows trivial behavior. Gauge theories in higher dimensions are treated within Migdal-Kadanoff approximation. We consider the gauge theory in the confinement phase. We demonstrate the existence of a non-analytical change from the short distance to long distance form in the entanglement entropy in such systems (d>2) reminiscent of a phase transition. The transition is manifested in nontrivial change in the RG flow of the character expansion coefficients defining the partition function.