Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity

TL;DR

This work analyzes entanglement thermodynamics for low-excitation states in holographic theories with higher-derivative gravity (Lovelock). Using Gauss–Bonnet corrections in 5D and cubic Lovelock terms in 7D, it derives holographic entanglement entropy and its variance for small subsystems (ball and stripe) and connects these results to boundary CFT central charges, illustrating how $\Delta S_A$ encodes central-charge data. It also develops a general Fefferman–Graham description for aAdS backgrounds to relate $\Delta S$ and $\Delta E$ to boundary stress-tensor perturbations, highlighting when a first-law-like relation $\Delta E = T_{ent} \Delta S$ can hold in various geometries. Overall, the paper extends holographic entanglement thermodynamics to higher-derivative gravity, showing how entanglement temperature and entropy fluctuations reflect CFT data and bulk couplings, and proposes a general framework for analyzing arbitrary low excitations.

Abstract

We investigate the entanglement temperature of a small scale subsystem in low excited states by using holographic method. Especially, we study the entanglement entropy and entanglement temperature in higher derivative gravities which are considered as low thermal excitation of pure AdS gravity. We find that the entanglement entropy are related to the central charges of boundary CFT. The relation between the variance of entanglement entropy and energy of a small scale subsystem has been also obtained. Furthermore, the relation is consistent with the first law-like relation that is proposed by Phys. Rev. Lett. 110, 091602 (2013). Finally, we derive the formula of the variance of entanglement entropy in general excited states in gravity background with the Fefferman-Graham coordinates and the entanglement temperature can be figured out in special case.