AdS plane waves and entanglement entropy

TL;DR

This work analyzes holographic entanglement entropy in AdS plane wave spacetimes dual to anisotropically excited CFTs with uniform lightcone momentum density $T_{++}$. Using covariant HRT, it distinguishes two strip orientations (Case A and Case B), deriving a logarithmic entanglement entropy in the $AdS_5$ case and revealing a size-dependent finite part in Case A that scales as $l^{2-d/2}$ (with $d$ the boundary dimension), including a log form at $d=4$, and a phase-transition-like behavior in Case B with a critical width $l_c \sim Q^{-1/d}$ for $d\ge 3$. The analysis is complemented by exact $d=2$ results, regularized geometries, and a physical interpretation linking the differences to the direction of energy flow and a finite correlation length, offering insights into hyperscaling-violating duals and possible connections to Fermi-surface physics. Overall, the paper provides concrete, analytic results for entanglement structure in anisotropically excited holographic systems and clarifies how geometry, dimensionality, and orientation of the energy flux shape quantum entanglement measures."

Abstract

AdS plane waves describe simple backgrounds which are dual to anisotropically excited systems with energy fluxes. Upon dimensional reduction, they reduce to hyperscaling violating spacetimes: in particular, the $AdS_5$ plane wave is known to exhibit logarithmic behavior of the entanglement entropy. In this paper, we carry out an extensive study of the holographic entanglement entropy for strip-shaped subsystems in AdS plane wave backgrounds. We find that the results depend crucially on whether the strip is parallel or orthogonal to the energy current. In the latter case, we show that there is a phenomenon analogous to a phase transition.

Figures (2)

• Figure 1: The two different choices of the strip subsystem $A$. The gray arrows represents the energy current. The left and right are called case A and case B, respectively.
• Figure 2: Numerical plots of the regularized areas of extremal surfaces as functions of the width $l=\sqrt{2}\Delta x^+=-\sqrt{2}\Delta x^-$ of $A$. We set $Q=R=1$. The left and right graph corresponds to the results for $d=3$ and $d=4$, respectively. In each graph, the blue curve corresponds to the connected surface in the pure AdS space while the red one to the connected one in the AdS plane wave. The area is regularized by subtracting the area of the disconnected surface given by $x^\pm=$constant.