On Holographic Entanglement Entropy with Second Order Excitations

Song He, Jia-Rui Sun, Hai-Qing Zhang

Published 2014-11-23Version 1

We study the low-energy quantum excitation corrections to the holographic entanglement entropy of the boundary CFT from the bulk gravitational perturbations up to second order. By focusing on the case when the boundary subsystem is a strip, we show that the bulk minimal surface can be expanded in terms of the conserved charges such as the mass, angular momentum and electric charge of the bulk AdS black brane when the black brane is a slightly perturbed geometry deviates from the pure AdS spacetime. We also calculate the energy of the subsystem in the CFT and argue that the first law-like relation for the subsystem should be satisfied at second order when the bulk geometry is stable under fluctuations at the same order.