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Title: Shape dependence of holographic Rényi entropy in general dimensions

Abstract

We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.

Authors:
 [1];  [2];  [3];  [4];  [5];  [2]
  1. Univ. Hamburg, Hamburg (Germany)
  2. Perimeter Institute for Theoretical Physics, Waterloo (Canada)
  3. Institute for Advanced Study, Princeton, NJ (United States)
  4. Perimeter Institute for Theoretical Physics, Waterloo (Canada); Univ. of Western Ontario, London (Canada)
  5. Perimeter Institute for Theoretical Physics, Waterloo (Canada); Scuola Normale Superiore, Pisa (Italy); INFN - Sezione di Pisa, Pisa (Italy)
Publication Date:
Research Org.:
Univ. Hamburg, Hamburg (Germany)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1358547
Grant/Contract Number:  
SC0009988
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: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT correspondence; conformal field theory; field theories in higher dimensions

Citation Formats

Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, and Myers, Robert C. Shape dependence of holographic Rényi entropy in general dimensions. United States: N. p., 2016. Web. doi:10.1007/JHEP11(2016)180.
Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, & Myers, Robert C. Shape dependence of holographic Rényi entropy in general dimensions. United States. doi:10.1007/JHEP11(2016)180.
Bianchi, Lorenzo, Chapman, Shira, Dong, Xi, Galante, Damián A., Meineri, Marco, and Myers, Robert C. Tue . "Shape dependence of holographic Rényi entropy in general dimensions". United States. doi:10.1007/JHEP11(2016)180. https://www.osti.gov/servlets/purl/1358547.
@article{osti_1358547,
title = {Shape dependence of holographic Rényi entropy in general dimensions},
author = {Bianchi, Lorenzo and Chapman, Shira and Dong, Xi and Galante, Damián A. and Meineri, Marco and Myers, Robert C.},
abstractNote = {We present a holographic method for computing the response of Rényi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for d = 3, · · · , 6 spacetime dimensions, and also evaluate analytically the limits where the Rényi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relation between the Rényi shape dependence and the conformal weight of the twist operator. As a result, we also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.},
doi = {10.1007/JHEP11(2016)180},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2016,
place = {United States},
year = {2016},
month = {11}
}

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