# The holographic dual of Renyi relative entropy

### APA

Moosa, M. (2019). The holographic dual of Renyi relative entropy. Perimeter Institute. https://pirsa.org/19100072

### MLA

Moosa, Mudassir. The holographic dual of Renyi relative entropy. Perimeter Institute, Oct. 11, 2019, https://pirsa.org/19100072

### BibTex

@misc{ pirsa_19100072, doi = {10.48660/19100072}, url = {https://pirsa.org/19100072}, author = {Moosa, Mudassir}, keywords = {Quantum Fields and Strings}, language = {en}, title = {The holographic dual of Renyi relative entropy}, publisher = {Perimeter Institute}, year = {2019}, month = {oct}, note = {PIRSA:19100072 see, \url{https://pirsa.org}} }

Mudassir Moosa Cornell University

## Abstract

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this talk, I will introduce a one-parameter generalization of the relative entropy which I will call 'refined' Renyi relative entropy. I will use this quantity to present a one-parameter generalization of the aforementioned known results about the relative entropy. I will also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.