PIRSA:19100072

The holographic dual of Renyi relative entropy

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

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

          @misc{ pirsa_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

Talk number
PIRSA:19100072
Collection
Talk Type
Subject
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.