Gravitational anomalies, entanglement entropy, and flat-space holography

TL;DR

This paper proposes a new method to compute entanglement entropy in Galilean conformal field theories using gravitational anomalies and contraction techniques, successfully reproducing known formulas and exploring new regimes in flat-space holography.

Contribution

It introduces a novel prescription for entanglement entropy in Galilean CFTs that connects gravitational anomalies with flat-space holography, extending previous results and exploring new regimes.

Findings

Reproduces the Cardy formula in the thermal limit.

Calculates entanglement entropy for flat-space cosmological solutions.

Provides interpretations for flat-space chiral gravity.

Abstract

We introduce a prescription to compute the entanglement entropy of Galilean conformal field theories by combining gravitational anomalies and an \.{I}n\"{o}n\"{u}-Wigner contraction. We find that our expression for the entanglement entropy in the thermal limit reproduces the Cardy formula for Galilean conformal field theories. Using this proposal, we calculate the entanglement entropy for a class of Galilean conformal field theories, which are believed to be dual to three-dimensional flat-space cosmological solutions. These geometries describe expanding (contracting) universes and can be viewed as the flat-space limit of rotating Ba\~nados-Teitelboim-Zanelli black holes. We show that our finding reduces, in the appropriate limits, to the results discussed in the literature and provide interpretations for the previously unexplored regimes, such as flat-space chiral gravity.