Thermal Corrections to R\'enyi Entropy in BMS Field Theory

TL;DR

This paper investigates thermal corrections to Rènyi entropy in BMS field theory within three-dimensional flat holography, employing replica trick and uniformizing map, and introduces an alternative entanglement entropy calculation method.

Contribution

It provides the first detailed calculation of thermal Rènyi entropy corrections in BMS field theory, enhancing understanding of flat holography and BMS symmetries.

Findings

Calculated thermal Rènyi entropy corrections using replica trick.

Validated results with an alternative entanglement entropy method.

Enhanced understanding of universal phenomena in flat holography.

Abstract

In the study of three-dimensional flat holography, the BMS field theory manifests the infinite-dimensional BMS$_3$ symmetry, a powerful tool in elucidating numerous universal phenomena. This paper explores a certain low-temperature limit of the BMS field theory. The primary focus lies in the calculation of the thermal correction to the R\'enyi entropy of the single interval on the cylinder from the replica trick and the uniformizing map. As a double check, an alternative method calculating the entanglement entropy is introduced, with the entanglement first law and the modular Hamiltonian.