# Entanglement Entropy in Flat Holography

## TL;DR

This paper develops a holographic method to compute entanglement and Rényi entropies in three-dimensional flat spacetime gravity theories, connecting boundary BMS symmetry with bulk geometric constructs.

## Contribution

It introduces a novel geometric approach for entanglement entropy in flat holography using null and spacelike geodesics, extending the Rindler method to BMS invariant theories.

## Key findings

- Holographic entanglement entropy is given by spacelike geodesic length.
- Null geodesics connect the geodesic to the boundary interval.
- The method applies to Einstein and Topologically Massive Gravity.

## Abstract

BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and R\'{e}nyi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.