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Title: Shape dependence of entanglement entropy in conformal field theories

Abstract

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient CT appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.

Authors:
 [1];  [1];  [1]
  1. Univ. of Illinois, Urbana, IL (United States), Dept. of Physics
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1395545
Grant/Contract Number:  
FG02-13ER42001; SC0009932
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: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; field theories in higher dimensions

Citation Formats

Faulkner, Thomas, Leigh, Robert G., and Parrikar, Onkar. Shape dependence of entanglement entropy in conformal field theories. United States: N. p., 2016. Web. https://doi.org/10.1007/JHEP04(2016)088.
Faulkner, Thomas, Leigh, Robert G., & Parrikar, Onkar. Shape dependence of entanglement entropy in conformal field theories. United States. https://doi.org/10.1007/JHEP04(2016)088
Faulkner, Thomas, Leigh, Robert G., and Parrikar, Onkar. Thu . "Shape dependence of entanglement entropy in conformal field theories". United States. https://doi.org/10.1007/JHEP04(2016)088. https://www.osti.gov/servlets/purl/1395545.
@article{osti_1395545,
title = {Shape dependence of entanglement entropy in conformal field theories},
author = {Faulkner, Thomas and Leigh, Robert G. and Parrikar, Onkar},
abstractNote = {Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient CT appearing in the two-point function of stress tensors in that CFT. As applications of our result, we prove the conjectured universality of the corner term coefficient σ/CT=π2/24 in d = 3 CFTs, and the holographic Mezei formula for entanglement entropy across deformed spheres.},
doi = {10.1007/JHEP04(2016)088},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2016,
place = {United States},
year = {2016},
month = {4}
}

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Works referenced in this record:

Building up spacetime with quantum entanglement
journal, June 2010


Entanglement entropy, conformal invariance and extrinsic geometry
journal, July 2008


Wess-Zumino Consistency Condition for Entanglement Entropy
journal, July 2012


Corner contributions to holographic entanglement entropy
journal, August 2015


A refinement of entanglement entropy and the number of degrees of freedom
journal, April 2013


On graviton non-gaussianities during inflation
journal, September 2011

  • Maldacena, Juan M.; Pimentel, Guilherme L.
  • Journal of High Energy Physics, Vol. 2011, Issue 9
  • DOI: 10.1007/JHEP09(2011)045

A note on CFT correlators in three dimensions
journal, July 2013

  • Giombi, Simone; Prakash, Shiroman; Yin, Xi
  • Journal of High Energy Physics, Vol. 2013, Issue 7
  • DOI: 10.1007/JHEP07(2013)105

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

On shape dependence and RG flow of entanglement entropy
journal, July 2012

  • Klebanov, Igor R.; Nishioka, Tatsuma; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)001

Holographic local quenches and entanglement density
journal, May 2013

  • Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2013, Issue 5
  • DOI: 10.1007/JHEP05(2013)080

Mutual information and the F-theorem
journal, October 2015

  • Casini, Horacio; Huerta, Marina; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)003

Spinning conformal correlators
journal, November 2011

  • Costa, Miguel S.; Penedones, João; Poland, David
  • Journal of High Energy Physics, Vol. 2011, Issue 11
  • DOI: 10.1007/JHEP11(2011)071

Bulk emergence and the RG flow of entanglement entropy
journal, May 2015


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


Entanglement entropy of gapped phases and topological order in three dimensions
journal, November 2011


Detecting Topological Order in a Ground State Wave Function
journal, March 2006


Topological Entanglement Entropy
journal, March 2006


Entanglement entropy for relevant and geometric perturbations
journal, February 2015

  • Rosenhaus, Vladimir; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)015

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

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


Bounds on corner entanglement in quantum critical states
journal, January 2016


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

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


On the duality condition for quantum fields
journal, January 1976

  • Bisognano, Joseph J.
  • Journal of Mathematical Physics, Vol. 17, Issue 3
  • DOI: 10.1063/1.522898

Aspects of holographic entanglement entropy
journal, August 2006


Integral geometry and holography
journal, October 2015

  • Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)175

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

Holography from conformal field theory
journal, October 2009


Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids
journal, May 2008


Entanglement entropy: a perturbative calculation
journal, December 2014

  • Rosenhaus, Vladimir; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)179

A holographic proof of the universality of corner entanglement for CFTs
journal, October 2015


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

OPE of the stress tensors and surface operators
journal, June 2015

  • Huang, Xing; Hung, Ling-Yan; Lin, Feng-Li
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)087

    Works referencing / citing this record:

    Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
    journal, September 2016

    • Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
    • Journal of High Energy Physics, Vol. 2016, Issue 9
    • DOI: 10.1007/jhep09(2016)038

    Modular Hamiltonians on the null plane and the Markov property of the vacuum state
    journal, August 2017

    • Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
    • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36
    • DOI: 10.1088/1751-8121/aa7eaa

    Universal divergence of the Rényi entropy of a thinly sliced torus at the Ising fixed point
    journal, July 2019

    • Kulchytskyy, Bohdan; Sierens, Lauren E. Hayward; Melko, Roger G.
    • Physical Review B, Vol. 100, Issue 4
    • DOI: 10.1103/physrevb.100.045139

    Relating bulk to boundary entanglement
    journal, December 2019


    Holographic proof of the quantum null energy condition
    journal, July 2016


    Energy density from second shape variations of the von Neumann entropy
    journal, October 2018

    • Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
    • Physical Review D, Vol. 98, Issue 8
    • DOI: 10.1103/physrevd.98.086013

    Universality of Squashed-Sphere Partition Functions
    journal, February 2019


    Rényi entropy and conformal defects
    text, January 2016

    • Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2016-05957