The holographic dual of Rényi relative entropy

Bao, Ning; Moosa, Mudassir; Shehzad, Ibrahim

doi:10.1007/JHEP08(2019)099

Title: The holographic dual of Rényi relative entropy

Journal Article · 20 August 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP08(2019)099 · OSTI ID:1566870

Bao, Ning ^[1];

^[2]; Shehzad, Ibrahim ^[2]

Berkeley Center for Theoretical Physics, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
Cornell Univ., Ithaca, NY (United States)

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.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21)

Grant/Contract Number:: SC0012704

OSTI ID:: 1566870

Report Number(s):: BNL--212134-2019-JAAM

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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