Comments on universal properties of entanglement entropy and bulk reconstruction

TL;DR

This paper explores the universal properties of entanglement entropy in holographic CFTs and their implications for bulk gravity reconstruction, highlighting the role of universal contributions and discrete parameters in the theory.

Contribution

It demonstrates the correspondence between universal entanglement entropy terms and the uniqueness of the graviton propagator in AdS, providing insights into bulk theory distinguishability.

Findings

Universal entanglement entropy contributions depend on discrete CFT parameters.

The first order change in entanglement entropy is universal for perturbed CFTs.

Entanglement data can potentially distinguish bulk theories with different higher curvature couplings.

Abstract

Entanglement entropy of holographic CFTs is expected to play a crucial role in the reconstruction of semiclassical bulk gravity. We consider the entanglement entropy of spherical regions of vacuum, which is known to contain universal contributions. After perturbing the CFT with a relevant scalar operator, also the first order change of this quantity gives a universal term which only depends on a discrete set of basic CFT parameters. We show that in gravity this statement corresponds to the uniqueness of the ghost-free graviton propagator on an AdS background geometry. While the gravitational dynamics in this context contains little information about the structure of the bulk theory, there is a discrete set of dimensionless parameters of the theory which determines the entanglement entropy. We argue that for every (not necessarily holographic) CFT, any reasonable gravity model can be used to compute this particular entanglement entropy. We elucidate how this statement is consistent with AdS/CFT and also give various generalizations. On the one hand this illustrates the remarkable usefulness of geometric concepts for understanding entanglement in general CFTs. On the other hand, it provides hints as to what entanglement data can be expected to provide enough information to distinguish, e.g., bulk theories with different higher curvature couplings.