Warped Entanglement Entropy

TL;DR

This paper explores the application of covariant holographic entanglement entropy to warped AdS3 spacetimes, showing that the entanglement entropy retains a universal CFT form under perturbations, and matches known central charge results.

Contribution

It extends the holographic entanglement entropy proposal to warped AdS3 geometries, deriving universal results and confirming the warping-dependent central charge matches previous findings.

Findings

Entanglement entropy retains a universal CFT form in warped AdS3.

Warping-dependent central charge matches previous calculations.

Results hold for large fiber coordinate separation and warped BTZ black holes.

Abstract

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1) isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds which are written as a real-line fibration over AdS$_2$. We then perturb away from this geometry by considering a warping parameter $a=1+\delta$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $\delta$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in $\delta$ and takes the universal form appropriate for two-dimensional CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.