The holographic dual of Rényi relative entropy
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 AdSRindler spacetime. Moreover, if the CFT has a semiclassical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this paper, we introduce a oneparameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a oneparameter generalization of the aforementioned known results about the relative entropy. We 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.
 Authors:

 Berkeley Center for Theoretical Physics, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Cornell Univ., Ithaca, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (SC21)
 OSTI Identifier:
 1566870
 Report Number(s):
 BNL2121342019JAAM
Journal ID: ISSN 10298479
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2019; Journal Issue: 8; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; AdSCFT Correspondence; Black Holes; Classical Theories of Gravity; Conformal Field Theory
Citation Formats
Bao, Ning, Moosa, Mudassir, and Shehzad, Ibrahim. The holographic dual of Rényi relative entropy. United States: N. p., 2019.
Web. doi:10.1007/JHEP08(2019)099.
Bao, Ning, Moosa, Mudassir, & Shehzad, Ibrahim. The holographic dual of Rényi relative entropy. United States. doi:10.1007/JHEP08(2019)099.
Bao, Ning, Moosa, Mudassir, and Shehzad, Ibrahim. Tue .
"The holographic dual of Rényi relative entropy". United States. doi:10.1007/JHEP08(2019)099. https://www.osti.gov/servlets/purl/1566870.
@article{osti_1566870,
title = {The holographic dual of Rényi relative entropy},
author = {Bao, Ning and Moosa, Mudassir and Shehzad, Ibrahim},
abstractNote = {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 AdSRindler spacetime. Moreover, if the CFT has a semiclassical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this paper, we introduce a oneparameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a oneparameter generalization of the aforementioned known results about the relative entropy. We 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.},
doi = {10.1007/JHEP08(2019)099},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 8,
volume = 2019,
place = {United States},
year = {2019},
month = {8}
}
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