# Entanglement entropy in conformal perturbation theory and the Einstein equation

### APA

Speranza, A. (2016). Entanglement entropy in conformal perturbation theory and the Einstein equation. Perimeter Institute. https://pirsa.org/16020011

### MLA

Speranza, Antony. Entanglement entropy in conformal perturbation theory and the Einstein equation. Perimeter Institute, Feb. 02, 2016, https://pirsa.org/16020011

### BibTex

@misc{ pirsa_PIRSA:16020011, doi = {10.48660/16020011}, url = {https://pirsa.org/16020011}, author = {Speranza, Antony}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Entanglement entropy in conformal perturbation theory and the Einstein equation}, publisher = {Perimeter Institute}, year = {2016}, month = {feb}, note = {PIRSA:16020011 see, \url{https://pirsa.org}} }

Antony Speranza University of Illinois Urbana-Champaign

## Abstract

For a CFT perturbed by a relevant operator, the entanglement entropy of a spherical region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion applies for excited states near the vacuum. I will describe a method due to Faulkner for calculating these entanglement entropies, and apply it in the limit of small sphere size. The motivation for these calculations is a recent proposal by Jacobson suggesting an equivalence between the Einstein equation and the "maximal vacuum entanglement hypothesis" for quantum gravity. This proposal relies on a conjecture about the behavior of entanglement entropies for small spheres. The calculations presented here suggest that this conjecture must be modified, but I will discuss how Jacobson's derivation still applies under the modified conjecture.