Warped Entanglement Entropy

TL;DR

The paper investigates holographic entanglement entropy in asymptotically warped AdS$_3$ spacetimes using the covariant HRT proposal. By perturbing around AdS$_3$ with warp factor $a=1+\delta$ and considering large fiber-coordinate separations, it derives a universal two-dimensional CFT form for entanglement entropy with central charges $c_L=c_R=\dfrac{3\ell a}{2G_N}$, matching Cardy-like expectations. Warped BTZ black holes are then analyzed to extract left- and right-moving temperatures, which, together with the central charge, reproduce the thermodynamic entropy via Cardy, reinforcing the WCFT/CFT intuition in the IR. The results support a controlled perturbative approach to warped holography and reveal how warped geometries mimic 2D CFT behavior in the IR while highlighting open questions about nonperturbative regimes and vacuum choice.

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 $a=1+δ$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $δ$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in $δ$ 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.

Figures (1)

• Figure 1: This is the global AdS$_3$ cylinder parameterized by the coordinates \ref{['globalfibered']}. The coordinates $t_g$ and $\theta_g$ represent the usual global coordinates. We will primarily consider sticking to a region of the boundary with $r=\infty$ for simplicity. This figure is taken from Anninos:2009zi.