Entanglement in Weakly Coupled Lattice Gauge Theories

TL;DR

This paper computes entanglement entropy in lattice Yang-Mills theories, revealing a universal logarithmic term at weak coupling due to soft mode entanglement, with results consistent with dual scalar theories.

Contribution

It provides a direct lattice gauge theory calculation showing the universal logarithmic entanglement term without relying on dualities.

Findings

Logarithmic term in entanglement entropy scales as (1/2) * dim(G) * log(e^2 r) in 2D.

The logarithmic term dominates the universal entanglement entropy.

Results agree with dual scalar theory for Maxwell in 2D.

Abstract

We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group $G$ contains a generic logarithmic term at sufficiently weak coupling $e$. In two spatial dimensions, for a region of linear size $r$, this term equals $\frac{1}{2} \dim(G) \log\left(e^2 r\right)$ and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.