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Title: 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 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 paper, we introduce a one-parameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a one-parameter 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:
 [1]; ORCiD logo [2];  [2]
  1. Berkeley Center for Theoretical Physics, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. 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 (SC-21)
OSTI Identifier:
1566870
Report Number(s):
BNL-212134-2019-JAAM
Journal ID: ISSN 1029-8479; TRN: US2001007
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; AdS-CFT 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. https://doi.org/10.1007/JHEP08(2019)099
Bao, Ning, Moosa, Mudassir, and Shehzad, Ibrahim. Tue . "The holographic dual of Rényi relative entropy". United States. https://doi.org/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 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 paper, we introduce a one-parameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a one-parameter 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)},
number = 8,
volume = 2019,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
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Cited by: 2 works
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Figures / Tables:

Figure 1 Figure 1: The pictorial representation of the construction of the statesmore » $ρ$ and $ρ$($n$) using a Euclidean path integral over $\mathcal{H}$$′$ = $S$1×$\mathbb{H}$d−1. The vertical direction denotes the direction along the $S$1 whereas the horizontal direction denotes the radial direction of $\mathbb{H}$d−1and we have suppressed the transverse d− 2 dimensions. (This figure is inspired by figure 1 of [2].)« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.