Charged structure constants from modularity

Das, Diptarka; Datta, Shouvik; Pal, Sridip

doi:10.1007/jhep11(2017)183

Title: Charged structure constants from modularity

Abstract

We derive a universal formula for the average heavy-heavy-light structure constants for 2d CFTs with non-vanishing u(1) charge. The derivation utilizes the modular properties of one-point functions on the torus. Refinements in N = 2 SCFTs, show that the resulting Cardy-like formula for the structure constants has precisely the same shifts in the central charge as that of the thermodynamic entropy found earlier. This analysis generalizes the recent results by Kraus and Maloney for CFTs with an additional global u(1) symmetry. Our results at large central charge are also shown to match with computations from the holographic dual, which suggest that the averaged CFT three-point coefficient also serves as a useful probe of detecting black hole hair.

Authors:

Das, Diptarka ^[1]; Datta, Shouvik ^[2];

^[1]

Univ. of California San Diego, La Jolla, CA (United States). Dept. of Physics
Eidgenossische Technische Hochschule, Zurich (Switzerland). Institut fur Theoretische Physik

Publication Date:: Mon Nov 27 00:00:00 EST 2017

Research Org.:: Univ. of California, San Diego, CA (United States)

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

OSTI Identifier:: 1504774

Grant/Contract Number:: SC0009919; PHY-160761

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: 2017; 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; 79 ASTRONOMY AND ASTROPHYSICS; Conformal Field Theory; AdS-CFT Correspondence; Black Holes

Citation Formats


                    Das, Diptarka, Datta, Shouvik, and Pal, Sridip. Charged structure constants from modularity.  United States: N. p., 2017. 
Web.  doi:10.1007/jhep11(2017)183.

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                    Das, Diptarka, Datta, Shouvik, & Pal, Sridip. Charged structure constants from modularity.  United States.  https://doi.org/10.1007/jhep11(2017)183

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                    Das, Diptarka, Datta, Shouvik, and Pal, Sridip. Mon .  
"Charged structure constants from modularity".  United States.  https://doi.org/10.1007/jhep11(2017)183.  https://www.osti.gov/servlets/purl/1504774.

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@article{osti_1504774,

  title        = {Charged structure constants from modularity},

  author       = {Das, Diptarka and Datta, Shouvik and Pal, Sridip},

  abstractNote = {We derive a universal formula for the average heavy-heavy-light structure constants for 2d CFTs with non-vanishing u(1) charge. The derivation utilizes the modular properties of one-point functions on the torus. Refinements in N = 2 SCFTs, show that the resulting Cardy-like formula for the structure constants has precisely the same shifts in the central charge as that of the thermodynamic entropy found earlier. This analysis generalizes the recent results by Kraus and Maloney for CFTs with an additional global u(1) symmetry. Our results at large central charge are also shown to match with computations from the holographic dual, which suggest that the averaged CFT three-point coefficient also serves as a useful probe of detecting black hole hair.},

  doi          = {10.1007/jhep11(2017)183},

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

  number       = 11,

  volume       = 2017,

  place        = {United States},

  year         = {Mon Nov 27 00:00:00 EST 2017},

  month        = {Mon Nov 27 00:00:00 EST 2017}

}

Copy to clipboard

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Title: Charged structure constants from modularity

Abstract

Citation Formats

Determinant formulae and unitarity for the N = 2 superconformal algebras in two dimensions or exact results on string compactification journal, May 1986

Operator content of two-dimensional conformally invariant theories journal, January 1986

Virasoro conformal blocks and thermality from classical background fields journal, November 2015

Constraints on 2d CFT partition functions journal, October 2013

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

What we don't know about BTZ black hole entropy journal, November 1998

Elliptic Genera and 3d Gravity journal, March 2016

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

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

The Weak Gravity Conjecture in three dimensions journal, October 2016

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

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

Wilson lines and entanglement entropy in higher spin gravity journal, October 2013

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

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

The string landscape, black holes and gravity as the weakest force journal, June 2007

Anti de Sitter space and holography journal, January 1998

Witten diagrams revisited: the AdS geometry of conformal blocks journal, January 2016

Modular Constraints on Calabi-Yau Compactifications journal, September 2013

Emergent space-time and the supersymmetric index journal, May 2016

Unravelling holographic entanglement entropy in higher spin theories journal, March 2015

Entanglement entropy and higher spin holography in AdS3 journal, April 2014

Universal bounds on charged states in 2d CFT and 3d gravity journal, August 2016

Higher spin black holes from CFT text, January 2012

The $\epsilon $-expansion from conformal field theory journal, July 2015

Emergent Spacetime and Holographic CFTs text, January 2011

Higher Spin Black Holes from CFT text, January 2012

Wilson Lines and Entanglement Entropy in Higher Spin Gravity text, January 2013

Entanglement Entropy and Higher Spin Holography in AdS$_3$ text, January 2013

Constraints on 2d CFT partition functions 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

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

Virasoro Conformal Blocks and Thermality from Classical Background Fields text, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks text, January 2015

Emergent space-time and the supersymmetric index text, January 2015

Holographic Conformal Partial Waves as Gravitational Open Wilson Networks text, January 2016

Witten Diagrams for Torus Conformal Blocks text, January 2017

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

Anti De Sitter Space And Holography text, January 1998

Determinant formulae and unitarity for the N = 2 superconformal algebras in two dimensions or exact results on string compactification journal, May 1986

A Universal Inequality for CFT and Quantum Gravity text, January 2009

A new spin on entanglement entropy text, January 2014

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

Growing extra dimensions in AdS/CFT journal, August 2019

Probing thermality beyond the diagonal journal, December 2018

Bound on asymptotics of magnitude of three point coefficients in 2D CFT journal, January 2020

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

Parity and the modular bootstrap journal, January 2018

BMS characters and modular invariance journal, July 2019

Structure constants from modularity in warped CFT journal, October 2019

Probing thermality beyond the diagonal text, January 2018

Parity and the modular bootstrap text, January 2018

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

BMS Characters and Modular Invariance text, January 2019

Structure Constants from Modularity in Warped CFT text, January 2019

Fast Conformal Bootstrap and Constraints on 3d Gravity text, January 2019

Growing Extra Dimensions in AdS/CFT text, January 2019

Bound on asymptotics of magnitude of three point coefficients in 2D CFT text, January 2019

Determinant formulae and unitarity for the N = 2 superconformal algebras in two dimensions or exact results on string compactification
journal, May 1986

Operator content of two-dimensional conformally invariant theories
journal, January 1986

Virasoro conformal blocks and thermality from classical background fields
journal, November 2015

Constraints on 2d CFT partition functions
journal, October 2013

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

What we don't know about BTZ black hole entropy
journal, November 1998

Elliptic Genera and 3d Gravity
journal, March 2016

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

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

The Weak Gravity Conjecture in three dimensions
journal, October 2016

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

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

Wilson lines and entanglement entropy in higher spin gravity
journal, October 2013

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

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

The string landscape, black holes and gravity as the weakest force
journal, June 2007

Anti de Sitter space and holography
journal, January 1998

Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

Modular Constraints on Calabi-Yau Compactifications
journal, September 2013

Emergent space-time and the supersymmetric index
journal, May 2016

Unravelling holographic entanglement entropy in higher spin theories
journal, March 2015

Entanglement entropy and higher spin holography in AdS3
journal, April 2014

Universal bounds on charged states in 2d CFT and 3d gravity
journal, August 2016

Higher spin black holes from CFT
text, January 2012

The $\epsilon $-expansion from conformal field theory
journal, July 2015

Emergent Spacetime and Holographic CFTs
text, January 2011

Higher Spin Black Holes from CFT
text, January 2012

Wilson Lines and Entanglement Entropy in Higher Spin Gravity
text, January 2013

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text, January 2013

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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

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

Virasoro Conformal Blocks and Thermality from Classical Background Fields
text, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
text, January 2015

Emergent space-time and the supersymmetric index
text, January 2015

Holographic Conformal Partial Waves as Gravitational Open Wilson Networks
text, January 2016

Witten Diagrams for Torus Conformal Blocks
text, January 2017

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

Anti De Sitter Space And Holography
text, January 1998

Determinant formulae and unitarity for the N = 2 superconformal algebras in two dimensions or exact results on string compactification
journal, May 1986

A Universal Inequality for CFT and Quantum Gravity
text, January 2009

A new spin on entanglement entropy
text, January 2014

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

Growing extra dimensions in AdS/CFT
journal, August 2019

Probing thermality beyond the diagonal
journal, December 2018

Bound on asymptotics of magnitude of three point coefficients in 2D CFT
journal, January 2020

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

Parity and the modular bootstrap
journal, January 2018

BMS characters and modular invariance
journal, July 2019

Structure constants from modularity in warped CFT
journal, October 2019

Probing thermality beyond the diagonal
text, January 2018

Parity and the modular bootstrap
text, January 2018

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

BMS Characters and Modular Invariance
text, January 2019

Structure Constants from Modularity in Warped CFT
text, January 2019

Fast Conformal Bootstrap and Constraints on 3d Gravity
text, January 2019

Growing Extra Dimensions in AdS/CFT
text, January 2019

Bound on asymptotics of magnitude of three point coefficients in 2D CFT
text, January 2019