On Holographic Entanglement Entropy with Second Order Excitations

TL;DR

This paper investigates second order perturbations in holographic entanglement entropy within AdS/CFT, demonstrating how conserved charges influence the minimal surface area and confirming thermodynamic relations at this order.

Contribution

It provides a detailed analysis of second order corrections to HEE and connects these to conserved charges and thermodynamic laws in the holographic framework.

Findings

HEE expanded in terms of conserved charges

First law-like thermodynamic relation verified at second order

HEE remains bounded if cosmic censorship holds

Abstract

We study the low-energy corrections to the holographic entanglement entropy (HEE) in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.