Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Pal, Sridip

doi:10.1007/JHEP01(2020)023

Title: Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Abstract

Here, we use methods inspired from complex Tauberian theorems to make progress in understanding the asymptotic behavior of the magnitude of heavy-light-heavy three point coefficients rigorously. The conditions and the precise sense of averaging, which can lead to exponential suppression of such coefficients are investigated. We derive various bounds for the typical average value of the magnitude of heavy-light-heavy three point coefficients and verify them numerically.

Authors:

^[1]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: 2020-01-07

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Simons Foundation

OSTI Identifier:: 1597248

Grant/Contract Number:: SC0009988; SC0009919

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: 2020; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal and W Symmetry; Conformal Field Theory

Citation Formats


                    Pal, Sridip. Bound on asymptotics of magnitude of three point coefficients in 2D CFT.  United States: N. p., 2020. 
Web.  doi:10.1007/JHEP01(2020)023.

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                    Pal, Sridip. Bound on asymptotics of magnitude of three point coefficients in 2D CFT.  United States.  https://doi.org/10.1007/JHEP01(2020)023

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                    Pal, Sridip. Tue .  
"Bound on asymptotics of magnitude of three point coefficients in 2D CFT".  United States.  https://doi.org/10.1007/JHEP01(2020)023.  https://www.osti.gov/servlets/purl/1597248.

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@article{osti_1597248,

  title        = {Bound on asymptotics of magnitude of three point coefficients in 2D CFT},

  author       = {Pal, Sridip},

  abstractNote = {Here, we use methods inspired from complex Tauberian theorems to make progress in understanding the asymptotic behavior of the magnitude of heavy-light-heavy three point coefficients rigorously. The conditions and the precise sense of averaging, which can lead to exponential suppression of such coefficients are investigated. We derive various bounds for the typical average value of the magnitude of heavy-light-heavy three point coefficients and verify them numerically.},

  doi          = {10.1007/JHEP01(2020)023},

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

  number       = 1,

  volume       = 2020,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Works referenced in this record:

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

Cardy, John L.
Nuclear Physics B, Vol. 270
DOI: 10.1016/0550-3213(86)90552-3

Modular constraints on conformal field theories with currents
journal, December 2017

Bae, Jin-Beom; Lee, Sungjay; Song, Jaewon
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/JHEP12(2017)045

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

Hartman, Thomas; Keller, Christoph A.; Stoica, Bogdan
Journal of High Energy Physics, Vol. 2014, Issue 9
DOI: 10.1007/JHEP09(2014)118

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
Nature, Vol. 452, Issue 7189
DOI: 10.1038/nature06838

Charged structure constants from modularity
text, January 2017

Das, Diptarka; Datta, Shouvik; Pal, Sridip
ETH Zurich
DOI: 10.3929/ethz-b-000220012

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

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/JHEP03(2019)075

A Tauberian Theorem for Partitions
journal, December 1941

Ingham, A. E.
The Annals of Mathematics, Vol. 42, Issue 5
DOI: 10.2307/1970462

Eigenstate thermalization hypothesis in conformal field theory
journal, March 2018

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, Issue 3
DOI: 10.1088/1742-5468/aab020

Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block
journal, August 2019

Kusuki, Yuya; Miyaji, Masamichi
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/JHEP08(2019)063

Does a Single Eigenstate Encode the Full Hamiltonian?
journal, April 2018

Garrison, James R.; Grover, Tarun
Physical Review X, Vol. 8, Issue 2
DOI: 10.1103/PhysRevX.8.021026

Growing extra dimensions in AdS/CFT
journal, August 2019

Alday, Luis F.; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/JHEP08(2019)084

Genus two modular bootstrap
journal, April 2019

Cho, Minjae; Collier, Scott; Yin, Xi
Journal of High Energy Physics, Vol. 2019, Issue 4
DOI: 10.1007/JHEP04(2019)022

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity
journal, January 2019

Kusuki, Yuya
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/JHEP01(2019)025

Modular invariance, tauberian theorems and microcanonical entropy
journal, October 2019

Mukhametzhanov, Baur; Zhiboedav, Alexander
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/JHEP10(2019)261

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

Hellerman, Simeon
Journal of High Energy Physics, Vol. 2011, Issue 8
DOI: 10.1007/JHEP08(2011)130

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: iii. a note on the sum function of the fourier coefficients of integral modular forms
journal, April 1940

Rankin, R. A.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 36, Issue 2
DOI: 10.1017/S0305004100017114

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

Collier, Scott; Gobeil, Yan; Maxfield, Henry
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/JHEP05(2019)212

Charged structure constants from modularity
journal, November 2017

Das, Diptarka; Datta, Shouvik; Pal, Sridip
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/JHEP11(2017)183

Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
journal, December 2019

Maxfield, Henry
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/JHEP12(2019)003

Modular bootstrap revisited
journal, September 2018

Collier, Scott; Lin, Ying-Hsuan; Yin, Xi
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/JHEP09(2018)061

A cardy formula for three-point coefficients or how the black hole got its spots
journal, May 2017

Kraus, Per; Maloney, Alexander
Journal of High Energy Physics, Vol. 2017, Issue 5
DOI: 10.1007/JHEP05(2017)160

Light-state dominance from the conformal bootstrap
journal, August 2019

Kraus, Per; Sivaramakrishnan, Allic
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/JHEP08(2019)013

A tauberian theorem for the conformal bootstrap
journal, December 2017

Qiao, Jiaxin; Rychkov, Slava
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/JHEP12(2017)119

Typicality and thermality in 2d CFT
journal, July 2019

Datta, Shouvik; Kraus, Per; Michel, Ben
Journal of High Energy Physics, Vol. 2019, Issue 7
DOI: 10.1007/JHEP07(2019)143

Analytic Euclidean bootstrap
journal, October 2019

Mukhametzhanov, Baur; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/JHEP10(2019)270

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms
journal, July 1939

Rankin, R. A.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 35, Issue 3
DOI: 10.1017/s0305004100021101

Critical Ising correlation functions in the plane and on the torus
journal, January 1987

Di Francesco, P.; Saleur, H.; Zuber, J. B.
Nuclear Physics B, Vol. 290
DOI: 10.1016/0550-3213(87)90202-1

Constraints on flavored 2d CFT partition functions
journal, February 2018

Dyer, Ethan; Fitzpatrick, A. Liam; Xin, Yuan
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/JHEP02(2018)148

Quantum statistical mechanics in a closed system
journal, February 1991

Deutsch, J. M.
Physical Review A, Vol. 43, Issue 4
DOI: 10.1103/PhysRevA.43.2046

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

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/JHEP02(2019)044

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: I. The zeros of the function on the line
journal, July 1939

Rankin, R. A.
Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 35, Issue 3
DOI: 10.1017/s0305004100021095

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

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
Unpublished
DOI: 10.13140/rg.2.2.12538.75203

Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT
text, January 2018

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
Unpublished
DOI: 10.13140/rg.2.2.32671.41129

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

Hartman, Thomas; Keller, Christoph A.; Stoica, Bogdan
arXiv
DOI: 10.48550/arxiv.1405.5137

Does a single eigenstate encode the full Hamiltonian?
text, January 2015

Garrison, James R.; Grover, Tarun
arXiv
DOI: 10.48550/arxiv.1503.00729

Eigenstate Thermalization Hypothesis in Conformal Field Theory
text, January 2016

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong
arXiv
DOI: 10.48550/arxiv.1610.00302

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

Maloney, Alexander; Ng, Gim Seng; Ross, Simon F.
arXiv
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

Light-state Dominance from the Conformal Bootstrap
text, January 2018

Kraus, Per; Sivaramakrishnan, Allic
arXiv
DOI: 10.48550/arxiv.1812.02226

Typicality and thermality in 2d CFT
text, January 2019

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

Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
text, January 2019

Mukhametzhanov, Baur; Zhiboedov, Alexander
arXiv
DOI: 10.48550/arxiv.1904.06359

Growing Extra Dimensions in AdS/CFT
text, January 2019

Alday, Luis F.; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1906.01477

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Title: Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Abstract

Citation Formats

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

Modular constraints on conformal field theories with currents journal, December 2017

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

Thermalization and its mechanism for generic isolated quantum systems journal, April 2008

Charged structure constants from modularity text, January 2017

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

A Tauberian Theorem for Partitions journal, December 1941

Eigenstate thermalization hypothesis in conformal field theory journal, March 2018

Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block journal, August 2019

Does a Single Eigenstate Encode the Full Hamiltonian? journal, April 2018

Growing extra dimensions in AdS/CFT journal, August 2019

Genus two modular bootstrap journal, April 2019

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity journal, January 2019

Modular invariance, tauberian theorems and microcanonical entropy journal, October 2019

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

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: iii. a note on the sum function of the fourier coefficients of integral modular forms journal, April 1940

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

Charged structure constants from modularity journal, November 2017

Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap journal, December 2019

Modular bootstrap revisited journal, September 2018

A cardy formula for three-point coefficients or how the black hole got its spots journal, May 2017

Light-state dominance from the conformal bootstrap journal, August 2019

A tauberian theorem for the conformal bootstrap journal, December 2017

Typicality and thermality in 2d CFT journal, July 2019

Analytic Euclidean bootstrap journal, October 2019

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms journal, July 1939

Critical Ising correlation functions in the plane and on the torus journal, January 1987

Constraints on flavored 2d CFT partition functions journal, February 2018

Quantum statistical mechanics in a closed system journal, February 1991

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

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: I. The zeros of the function on the line journal, July 1939

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

Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT text, January 2018

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

Does a single eigenstate encode the full Hamiltonian? text, January 2015

Eigenstate Thermalization Hypothesis in Conformal Field Theory text, January 2016

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

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

Light-state Dominance from the Conformal Bootstrap text, January 2018

Typicality and thermality in 2d CFT text, January 2019

Modular Invariance, Tauberian Theorems, and Microcanonical Entropy text, January 2019

Growing Extra Dimensions in AdS/CFT text, January 2019

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

Modular constraints on conformal field theories with currents
journal, December 2017

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

Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008

Charged structure constants from modularity
text, January 2017

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

A Tauberian Theorem for Partitions
journal, December 1941

Eigenstate thermalization hypothesis in conformal field theory
journal, March 2018

Entanglement entropy, OTOC and bootstrap in 2D CFTs from Regge and light cone limits of multi-point conformal block
journal, August 2019

Does a Single Eigenstate Encode the Full Hamiltonian?
journal, April 2018

Growing extra dimensions in AdS/CFT
journal, August 2019

Genus two modular bootstrap
journal, April 2019

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity
journal, January 2019

Modular invariance, tauberian theorems and microcanonical entropy
journal, October 2019

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

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: iii. a note on the sum function of the fourier coefficients of integral modular forms
journal, April 1940

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

Charged structure constants from modularity
journal, November 2017

Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
journal, December 2019

Modular bootstrap revisited
journal, September 2018

A cardy formula for three-point coefficients or how the black hole got its spots
journal, May 2017

Light-state dominance from the conformal bootstrap
journal, August 2019

A tauberian theorem for the conformal bootstrap
journal, December 2017

Typicality and thermality in 2d CFT
journal, July 2019

Analytic Euclidean bootstrap
journal, October 2019

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms
journal, July 1939

Critical Ising correlation functions in the plane and on the torus
journal, January 1987

Constraints on flavored 2d CFT partition functions
journal, February 2018

Quantum statistical mechanics in a closed system
journal, February 1991

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

Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: I. The zeros of the function on the line
journal, July 1939

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

Generalized Gibbs Ensemble and the Statistics of KdV Charges in 2D CFT
text, January 2018

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

Does a single eigenstate encode the full Hamiltonian?
text, January 2015

Eigenstate Thermalization Hypothesis in Conformal Field Theory
text, January 2016

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

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

Light-state Dominance from the Conformal Bootstrap
text, January 2018

Typicality and thermality in 2d CFT
text, January 2019

Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
text, January 2019

Growing Extra Dimensions in AdS/CFT
text, January 2019