Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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]
+ Show Author Affiliations
  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)
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.
Copy to clipboard
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. https://doi.org/10.1007/JHEP11(2016)180
Copy to clipboard
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. https://doi.org/10.1007/JHEP11(2016)180. https://www.osti.gov/servlets/purl/1358547.
Copy to clipboard
@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 = {Tue Nov 29 00:00:00 EST 2016},
month = {Tue Nov 29 00:00:00 EST 2016}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/JHEP11(2016)180
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 35 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Evolution of entanglement entropy in one-dimensional systems
journal, April 2005

Entanglement Entropy and Quantum Field Theory: a Non-Technical Introduction
journal, June 2006

  • Calabrese, Pasquale; Cardy, John
  • International Journal of Quantum Information, Vol. 04, Issue 03
  • DOI: 10.1142/S021974990600192X

Building up spacetime with quantum entanglement
journal, June 2010

On the architecture of spacetime geometry
journal, October 2014

Cool horizons for entangled black holes
journal, August 2013

Entanglement Equilibrium and the Einstein Equation
journal, May 2016

Form Factors of Branch-Point Twist Fields in Quantum Integrable Models and Entanglement Entropy
journal, October 2007

  • Cardy, J. L.; Castro-Alvaredo, O. A.; Doyon, B.
  • Journal of Statistical Physics, Vol. 130, Issue 1
  • DOI: 10.1007/s10955-007-9422-x

Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations
journal, April 2010

Anomalies in the entanglement properties of the square-lattice Heisenberg model
journal, October 2011

Corner contribution to the entanglement entropy of an O (3) quantum critical point in 2 + 1 dimensions
journal, June 2014

  • Kallin, A. B.; Stoudenmire, E. M.; Fendley, P.
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 6
  • DOI: 10.1088/1742-5468/2014/06/P06009

Measuring Entanglement Entropy of a Generic Many-Body System with a Quantum Switch
journal, July 2012

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Aspects of holographic entanglement entropy
journal, August 2006

A covariant holographic entanglement entropy proposal
journal, July 2007

  • Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2007, Issue 07
  • DOI: 10.1088/1126-6708/2007/07/062

On holographic entanglement entropy and higher curvature gravity
journal, April 2011

  • Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2011, Issue 4
  • DOI: 10.1007/JHEP04(2011)025

Holographic entanglement entropy in Lovelock gravities
journal, July 2011

  • de Boer, Jan; Kulaxizi, Manuela; Parnachev, Andrei
  • Journal of High Energy Physics, Vol. 2011, Issue 7
  • DOI: 10.1007/JHEP07(2011)109

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Generalized entropy and higher derivative gravity
journal, March 2014

Quantum corrections to holographic entanglement entropy
journal, November 2013

  • Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)074

Generalized gravitational entropy
journal, August 2013

  • Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)090

The gravity dual of Rényi entropy
journal, August 2016

Towards a derivation of holographic entanglement entropy
journal, May 2011

  • Casini, Horacio; Huerta, Marina; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)036

Holographic calculations of Rényi entropy
journal, December 2011

  • Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)047

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories
journal, June 2016

Gravity duals of boundary cones
journal, September 2016

Rényi entropy and conformal defects
journal, July 2016

  • Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)076

Universality of Corner Entanglement in Conformal Field Theories
journal, July 2015

Universal entanglement for higher dimensional cones
journal, December 2015

On the shape dependence of Entanglement Entropy
journal, December 2015

On shape dependence of holographic mutual information in AdS4
journal, February 2015

  • Fonda, Piermarco; Giomi, Luca; Salvio, Alberto
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)005

On shape dependence of holographic entanglement entropy in AdS4/CFT3
journal, December 2015

  • Fonda, Piermarco; Seminara, Domenico; Tonni, Erik
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)037

Conformal invariance and surface critical behavior
journal, November 1984

Conformal field theories near a boundary in general dimensions
journal, September 1995

Defects in conformal field theory
journal, April 2016

  • Billò, Marco; Gonçalves, Vasco; Lauria, Edoardo
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)091

Universality in the geometric dependence of Rényi entropy
journal, January 2015

  • Lewkowycz, Aitor; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)080

Universal corner entanglement from twist operators
journal, September 2015

  • Bueno, Pablo; Myers, Robert C.; Witczak-Krempa, William
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)091

Shape dependence of entanglement entropy in conformal field theories
journal, April 2016

  • Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)088

Black holes in quasi-topological gravity
journal, August 2010

  • Myers, Robert C.; Robinson, Brandon
  • Journal of High Energy Physics, Vol. 2010, Issue 8
  • DOI: 10.1007/JHEP08(2010)067

Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
journal, March 2001

  • de Haro, Sebastian; Skenderis, Kostas; Solodukhin, Sergey N.
  • Communications in Mathematical Physics, Vol. 217, Issue 3
  • DOI: 10.1007/s002200100381

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions
journal, January 1997

Holographic GB gravity in arbitrary dimensions
journal, March 2010

  • Buchel, Alex; Escobedo, Jorge; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2010, Issue 3
  • DOI: 10.1007/JHEP03(2010)111

Viscosity Bound and Causality Violation
journal, May 2008

Causality of holographic hydrodynamics
journal, August 2009

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

Causality constraints on corrections to the graviton three-point coupling
journal, February 2016

  • Camanho, Xián O.; Edelstein, José D.; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)020

Holographic c-theorems in arbitrary dimensions
journal, January 2011

Gravitation from entanglement in holographic CFTs
journal, March 2014

  • Faulkner, Thomas; Guica, Monica; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)051

Exact results for the entanglement entropy and the energy radiated by a quark
journal, May 2014

  • Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)025

Exact Bremsstrahlung Function in N = 2 Superconformal Field Theories
journal, February 2016

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

Rényi entropy, stationarity, and entanglement of the conformal scalar
journal, March 2015

  • Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)075

Conformal collider physics: energy and charge correlations
journal, May 2008

Entanglement entropy in the O ( N ) model
journal, September 2009

Holographic phases of Rényi entropies
journal, December 2013

  • Belin, Alexandre; Maloney, Alexander; Matsuura, Shunji
  • Journal of High Energy Physics, Vol. 2013, Issue 12
  • DOI: 10.1007/JHEP12(2013)050
    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Emitted radiation and geometry
    journal, January 2020

    • Bianchi, L.; Billò, M.; Galvagno, F.
    • Journal of High Energy Physics, Vol. 2020, Issue 1
    • DOI: 10.1007/jhep01(2020)075

    Casimir effect, Weyl anomaly and displacement operator in boundary conformal field theory
    journal, July 2019

    All higher-curvature gravities as Generalized quasi-topological gravities
    journal, November 2019

    • Bueno, Pablo; Cano, Pablo A.; Moreno, Javier
    • Journal of High Energy Physics, Vol. 2019, Issue 11
    • DOI: 10.1007/jhep11(2019)062

    Universality at large transverse spin in defect CFT
    text, January 2018

    • Lemos, Madalena; Liendo, Pedro; Meineri, Marco
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2018-03901

    Holographic studies of Einsteinian cubic gravity
    text, January 2018

    Exact Bremsstrahlung functions in ABJM theory
    text, January 2018

    All higher-curvature gravities as Generalized quasi-topological gravities
    text, January 2019

    Emitted Radiation and Geometry
    text, January 2019

      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: