# Modular Hamiltonian of a chiral fermion on the torus

## TL;DR

This paper computes the modular Hamiltonian for a chiral fermion on a torus at finite temperature using a simple image method, revealing non-locality even for single intervals, a novel finding in the field.

## Contribution

It introduces a straightforward method to derive the modular Hamiltonian for a chiral fermion on a torus, highlighting its non-local nature even in simple cases.

## Key findings

- Modular Hamiltonian is non-local for a single interval.
- Method based on images is simple and potentially generalizable.
- First example of non-local modular Hamiltonian in this context.

## Abstract

We consider a chiral fermion at non-zero temperature on a circle (i.e., on a torus in the Euclidean formalism) and compute the modular Hamiltonian corresponding to a subregion of the circle. We do this by a very simple procedure based on the method of images, which is presumably generalizable to other situations. Our result is non-local even for a single interval, and even for Neveu-Schwarz boundary conditions. To the best of our knowledge, there are no previous examples of a modular Hamiltonian with this behavior.