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Title: Shape dependence of holographic Rényi entropy in general dimensions

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:
Grant/Contract Number:
SC0009988
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
Research Org:
Univ. Hamburg, Hamburg (Germany)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
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
OSTI Identifier:
1358547

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., 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.. 2016. "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}
}