Shape dependence of holographic Rényi entropy in general dimensions

Bianchi, Lorenzo; Chapman, Shira; Dong, Xi; Galante, Damián A.; Meineri, Marco; Myers, Robert C.

doi:10.1007/JHEP11(2016)180

Title: Shape dependence of holographic Rényi entropy in general dimensions

Journal Article · Tue Nov 29 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP11(2016)180· OSTI ID:1358547

Bianchi, Lorenzo ^[1]; Chapman, Shira ^[2]; Dong, Xi ^[3]; Galante, Damián A. ^[4]; Meineri, Marco ^[5]; Myers, Robert C. ^[2]

Univ. Hamburg, Hamburg (Germany)
Perimeter Institute for Theoretical Physics, Waterloo (Canada)
Institute for Advanced Study, Princeton, NJ (United States)
Perimeter Institute for Theoretical Physics, Waterloo (Canada); Univ. of Western Ontario, London (Canada)
Perimeter Institute for Theoretical Physics, Waterloo (Canada); Scuola Normale Superiore, Pisa (Italy); INFN - Sezione di Pisa, Pisa (Italy)

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.

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Research Organization:: Univ. Hamburg, Hamburg (Germany)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0009988

OSTI ID:: 1358547

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 11; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 35 works

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