Virasoro conformal blocks and thermality from classical background fields

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.

doi:10.1007/JHEP11(2015)200

Title: Virasoro conformal blocks and thermality from classical background fields

Abstract

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. Furthermore, we comment on the implications of our results for the universality of black hole thermality in AdS₃ , or equivalently, the eigenstate thermalization hypothesis for CFT₂ at large central charge.

Authors:

Fitzpatrick, A. Liam ^[1]; Kaplan, Jared ^[2]; Walters, Matthew T. ^[3]

Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Johns Hopkins Univ., Baltimore, MD (United States)
Boston Univ., Boston, MA (United States)

Publication Date:: Mon Nov 30 00:00:00 EST 2015

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1238365

Report Number(s):: SLAC-PUB-16625
Journal ID: ISSN 1029-8479; PII: 2614

Grant/Contract Number:: AC03-76SF00515

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: 2015; Journal Issue: 11; 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; conformal and W Symmetry

Citation Formats


                    Fitzpatrick, A. Liam, Kaplan, Jared, and Walters, Matthew T. Virasoro conformal blocks and thermality from classical background fields.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP11(2015)200.

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                    Fitzpatrick, A. Liam, Kaplan, Jared, & Walters, Matthew T. Virasoro conformal blocks and thermality from classical background fields.  United States.  https://doi.org/10.1007/JHEP11(2015)200

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                    Fitzpatrick, A. Liam, Kaplan, Jared, and Walters, Matthew T. Mon .  
"Virasoro conformal blocks and thermality from classical background fields".  United States.  https://doi.org/10.1007/JHEP11(2015)200.  https://www.osti.gov/servlets/purl/1238365.

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@article{osti_1238365,

  title        = {Virasoro conformal blocks and thermality from classical background fields},

  author       = {Fitzpatrick, A. Liam and Kaplan, Jared and Walters, Matthew T.},

  abstractNote = {We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. Furthermore, we comment on the implications of our results for the universality of black hole thermality in AdS3 , or equivalently, the eigenstate thermalization hypothesis for CFT2 at large central charge.},

  doi          = {10.1007/JHEP11(2015)200},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 11,

  volume       = 2015,

  place        = {United States},

  year         = {Mon Nov 30 00:00:00 EST 2015},

  month        = {Mon Nov 30 00:00:00 EST 2015}

}

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text, January 2018

Poland, David; Rychkov, Slava; Vichi, Alessandro
arXiv
DOI: 10.48550/arxiv.1805.04405

Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
text, January 2018

Kusuki, Yuya
arXiv
DOI: 10.48550/arxiv.1806.04352

c-Recursion for multi-point superconformal blocks. NS sector
text, January 2018

Belavin, V. A.; Geiko, R. V.
arXiv
DOI: 10.48550/arxiv.1806.09563

A theory of reparameterizations for AdS$_3$ gravity
text, January 2018

Cotler, Jordan; Jensen, Kristan
arXiv
DOI: 10.48550/arxiv.1808.03263

The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
preprint, January 2018

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared
arXiv
DOI: 10.48550/arxiv.1810.02436

Scrambling time from local perturbations of the rotating BTZ black hole
text, January 2018

Štikonas, Andrius
arXiv
DOI: 10.48550/arxiv.1810.06110

Thermal Correlation Functions of KdV Charges in 2D CFT
text, January 2018

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
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DOI: 10.48550/arxiv.1810.11053

Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
text, January 2018

Collier, Scott; Gobeil, Yan; Maxfield, Henry
arXiv
DOI: 10.48550/arxiv.1811.05710

Entanglement and chaos in warped conformal field theories
text, January 2018

Apolo, Luis; He, Song; Song, Wei
arXiv
DOI: 10.48550/arxiv.1812.10456

Holographic dual of the five-point conformal block
text, January 2019

Parikh, Sarthak
arXiv
DOI: 10.48550/arxiv.1901.01267

Phases of scrambling in eigenstates
text, January 2019

Anous, Tarek; Sonner, Julian
arXiv
DOI: 10.48550/arxiv.1903.03143

Typicality and thermality in 2d CFT
text, January 2019

Datta, Shouvik; Kraus, Per; Michel, Ben
arXiv
DOI: 10.48550/arxiv.1904.00668

Thermal Decay without Information Loss in Horizonless Microstate Geometries
text, January 2019

Bena, Iosif; Heidmann, Pierre; Monten, Ruben
arXiv
DOI: 10.48550/arxiv.1905.05194

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Title: Virasoro conformal blocks and thermality from classical background fields

Abstract

Citation Formats

Quantum statistical mechanics in a closed system journal, February 1991

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Anti de Sitter space and holography journal, January 1998

Gauge theory correlators from non-critical string theory journal, May 1998

Tensor representations of conformal algebra and conformally covariant operator product expansion journal, March 1973

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

Holography from conformal field theory journal, October 2009

The bootstrap program for boundary CFT d journal, July 2013

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Convexity and liberation at large spin journal, November 2013

Conformal blocks in the large D limit journal, August 2013

Higher-spin correlators journal, October 2013

N = 4 Superconformal Bootstrap journal, August 2013

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions journal, September 2014

Conformal bootstrap, universality and gravitational scattering journal, December 2015

Universality of long-distance AdS physics from the CFT bootstrap journal, August 2014

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

Quantum entanglement of localized excited states at finite temperature journal, January 2015

Generalized gravitational entropy journal, August 2013

Worldline approach to semi-classical conformal blocks journal, July 2015

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory journal, September 2015

Holographic entanglement entropy from 2d CFT: heavy states and local quenches journal, February 2015

A universal inequality for CFT and quantum gravity journal, August 2011

Universal spectrum of 2d conformal field theory in the large c limit journal, September 2014

Poincaré series, 3D gravity and CFT spectroscopy journal, February 2015

Black hole in three-dimensional spacetime journal, September 1992

Conformal four point functions and the operator product expansion journal, April 2001

Conformal partial waves and the operator product expansion journal, February 2004

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude journal, September 1984

Conformal symmetry in two-dimensional space: Recursion representation of conformal block journal, October 1987

Writing CFT correlation functions as AdS scattering amplitudes journal, March 2011

A natural language for AdS/CFT correlators journal, November 2011

Towards Feynman rules for Mellin amplitudes in AdS/CFT journal, October 2011

Weyl anomaly induced stress tensors in general manifolds journal, February 2014

One-loop partition functions of 3D gravity journal, August 2008

Partition functions of three-dimensional pure gravity journal, January 2008

Quantum corrections to holographic entanglement entropy journal, November 2013

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks journal, July 2015

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion text, January 1973

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion text, January 1971

Holography from Conformal Field Theory text, January 2009

More Holography from Conformal Field Theory text, January 2010

Effective Conformal Theory and the Flat-Space Limit of AdS text, January 2010

Chiral anomalies and AdS/CMT in two dimensions text, January 2010

Emergent Spacetime and Holographic CFTs text, January 2011

A Natural Language for AdS/CFT Correlators text, January 2011

Analyticity and the Holographic S-Matrix text, January 2011

The Bootstrap Program for Boundary CFT_d text, January 2012

Generalized gravitational entropy text, January 2013

Conformal Blocks in the Large D Limit text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Universality of Long-Distance AdS Physics from the CFT Bootstrap text, January 2014

Universal Spectrum of 2d Conformal Field Theory in the Large c Limit text, January 2014

Poincare Series, 3D Gravity and CFT Spectroscopy text, January 2014

Lessons from crossing symmetry at large N preprint, January 2014

Conformal Bootstrap, Universality and Gravitational Scattering text, January 2014

Worldline approach to semi-classical conformal blocks preprint, January 2015

Aspects of Holographic Entanglement Entropy text, January 2006

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit journal, January 2019

Note on ETH of descendant states in 2D CFT journal, January 2019

Probing typical black hole microstates journal, January 2020

Vacuum block thermalization in semi-classical 2d CFT journal, February 2019

Thermal correlation functions of KdV charges in 2D CFT journal, February 2019

Universality of quantum information in chaotic CFTs journal, March 2018

Generalized Gibbs ensemble and the statistics of KdV charges in 2D CFT journal, March 2019

Correlation functions of warped CFT journal, April 2018

Entanglement and chaos in warped conformal field theories journal, April 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations journal, May 2018

Quantum Regge trajectories and the Virasoro analytic bootstrap journal, May 2019

Spinning Witten diagrams journal, June 2017

The bulk-to-boundary propagator in black hole microstate backgrounds journal, June 2019

An inelastic bound on chaos journal, July 2019

On the universality of late-time correlators in semi-classical 2d CFTs journal, August 2018

c-Recursion for multi-point superconformal blocks. NS sector journal, August 2018

Quantum statistical mechanics in a closed system
journal, February 1991

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Anti de Sitter space and holography
journal, January 1998

Gauge theory correlators from non-critical string theory
journal, May 1998

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

Holography from conformal field theory
journal, October 2009

The bootstrap program for boundary CFT d
journal, July 2013

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Convexity and liberation at large spin
journal, November 2013

Conformal blocks in the large D limit
journal, August 2013

Higher-spin correlators
journal, October 2013

$N = 4$ Superconformal Bootstrap
journal, August 2013

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions
journal, September 2014

Conformal bootstrap, universality and gravitational scattering
journal, December 2015

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

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

Quantum entanglement of localized excited states at finite temperature
journal, January 2015

Generalized gravitational entropy
journal, August 2013

Worldline approach to semi-classical conformal blocks
journal, July 2015

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
journal, September 2015

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

A universal inequality for CFT and quantum gravity
journal, August 2011

Universal spectrum of 2d conformal field theory in the large c limit
journal, September 2014

Poincaré series, 3D gravity and CFT spectroscopy
journal, February 2015

Black hole in three-dimensional spacetime
journal, September 1992

Conformal four point functions and the operator product expansion
journal, April 2001

Conformal partial waves and the operator product expansion
journal, February 2004

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude
journal, September 1984

Conformal symmetry in two-dimensional space: Recursion representation of conformal block
journal, October 1987

Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011

A natural language for AdS/CFT correlators
journal, November 2011

Towards Feynman rules for Mellin amplitudes in AdS/CFT
journal, October 2011

Weyl anomaly induced stress tensors in general manifolds
journal, February 2014

One-loop partition functions of 3D gravity
journal, August 2008

Partition functions of three-dimensional pure gravity
journal, January 2008

Quantum corrections to holographic entanglement entropy
journal, November 2013

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks
journal, July 2015

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion
text, January 1973

Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion
text, January 1971

Holography from Conformal Field Theory
text, January 2009

More Holography from Conformal Field Theory
text, January 2010

Effective Conformal Theory and the Flat-Space Limit of AdS
text, January 2010

Chiral anomalies and AdS/CMT in two dimensions
text, January 2010

Emergent Spacetime and Holographic CFTs
text, January 2011

A Natural Language for AdS/CFT Correlators
text, January 2011

Analyticity and the Holographic S-Matrix
text, January 2011

The Bootstrap Program for Boundary CFT_d
text, January 2012

Generalized gravitational entropy
text, January 2013

Conformal Blocks in the Large D Limit
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Universality of Long-Distance AdS Physics from the CFT Bootstrap
text, January 2014

Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
text, January 2014

Poincare Series, 3D Gravity and CFT Spectroscopy
text, January 2014

Lessons from crossing symmetry at large N
preprint, January 2014

Conformal Bootstrap, Universality and Gravitational Scattering
text, January 2014

Worldline approach to semi-classical conformal blocks
preprint, January 2015

Aspects of Holographic Entanglement Entropy
text, January 2006

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit
journal, January 2019

Note on ETH of descendant states in 2D CFT
journal, January 2019

Probing typical black hole microstates
journal, January 2020

Vacuum block thermalization in semi-classical 2d CFT
journal, February 2019

Thermal correlation functions of KdV charges in 2D CFT
journal, February 2019

Universality of quantum information in chaotic CFTs
journal, March 2018

Generalized Gibbs ensemble and the statistics of KdV charges in 2D CFT
journal, March 2019

Correlation functions of warped CFT
journal, April 2018

Entanglement and chaos in warped conformal field theories
journal, April 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations
journal, May 2018

Quantum Regge trajectories and the Virasoro analytic bootstrap
journal, May 2019

Spinning Witten diagrams
journal, June 2017

The bulk-to-boundary propagator in black hole microstate backgrounds
journal, June 2019

An inelastic bound on chaos
journal, July 2019

On the universality of late-time correlators in semi-classical 2d CFTs
journal, August 2018

c-Recursion for multi-point superconformal blocks. NS sector
journal, August 2018

Witten diagrams for torus conformal blocks
journal, September 2017

Holographic duals of large-c torus conformal blocks
journal, October 2017

Rényi mutual information in holographic warped CFTs
journal, October 2019