# Entanglement Entropy with Background Gauge Fields

## TL;DR

This paper investigates how constant background gauge fields affect entanglement and Renyi entropies of Dirac fermions on a 2D torus, revealing distinct behaviors in different temperature regimes and novel physical insights.

## Contribution

It provides detailed formulas and computations for entanglement measures in the presence of gauge fields, highlighting new physical phenomena at various temperature limits.

## Key findings

- High temperature limit shows non-trivial, modulus-dependent behavior.
- Entanglement properties differ significantly between low and high temperature regimes.
- Background gauge fields induce novel physical effects in entanglement entropy.

## Abstract

We study the entanglement entropy, the R\'enyi entropy, and the mutual (R\'enyi) information of Dirac fermions on a 2 dimensional torus in the presence of constant gauge fields. We derive their general formulas using the equivalence between twisted boundary conditions and the background gauge fields. Novel and interesting physical consequences have been presented in arXiv:1705.01859. Here we provide detailed computations of the entropies and mutual information in a low temperature limit, a large radius limit, and a high temperature limit. The high temperature limit reveals rather different physical properties compared to those of the low temperature one: there exist two non-trivial limits that depend on a modulus parameter and are not smoothly connected.