Fixing the AdS$_3$ metric from the pure state entanglement entropies of CFT$_2$

TL;DR

This paper demonstrates that the dual geometry of a perturbed CFT$_2$ can be uniquely reconstructed as asymptotically AdS$_3$ using entanglement entropy data via the RT formula, applicable in static and covariant cases.

Contribution

It provides a method to fix the AdS$_3$ metric from pure state entanglement entropies, extending previous work to include perturbed states and covariant scenarios.

Findings

Dual geometry is uniquely determined as asymptotically AdS$_3$

Pure AdS$_3$ recovered in the massless limit

Method applies to both static and covariant cases

Abstract

In this paper, based on RT formula, by identifying the pure state UV and IR entanglement entropies of a perturbed CFT$_2$ with geodesic lengths in the bulk, we demonstrate that the dual geometry is uniquely determined to be asymptotically AdS$_3$. The pure AdS$_3$ geometry is recovered by taking the massless limit of the system. Our derivations hold in both static and covariant scenarios.