Holographic Entanglement Entropy in flat limit of the Generalized Minimal Massive Gravity model

TL;DR

This paper investigates holographic entanglement entropy in the flat limit of GMMG, demonstrating agreement between bulk gravity calculations and BMSFT field theory results, thus supporting the flat space holography correspondence.

Contribution

It provides the first calculation of holographic entanglement entropy for GMMG in flat space, confirming the BMSFT duality and extending flat space holography insights.

Findings

Entanglement entropy matches between gravity and field theory calculations.

Supports BMS/flat space holography correspondence.

Calculations performed for zero and non-zero temperature cases.

Abstract

Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in asymptotically $AdS_3$ background, and have shown that the theory is free of negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned bulk-boundary unitarity clash. Here instead of $AdS_3$ space we consider asymptotically flat space, and study this model in the flat limit. The dual field theory of GMMG in the flat limit is a $BMS_3$ invariant field theory, dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro algebra. In fact here we present an evidence for this claim. Entanglement entropy of GMMG is calculated in the background in the flat null infinity. Our evidence for mentioned claim is the result for entanglement entropy in filed theory side and in the bulk (in the gravity side). At first using Cardy formula and Rindler transformation, we calculate entanglement entropy of BMSFT in three different cases. Zero temperature on the plane and on the cylinder, and non-zero temperature case. Then we obtain the entanglement entropy in the bulk. Our results in gravity side are exactly in agreement with field theory calculations.