Built on

T. Anous and J. Sonner, “Phases of scrambling in eigenstates,” SciPost Phys
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, “Modular invariance, tauberian theorems and microcanonical entropy,” JHEP
Original
1904
Earlier work this paper cites.
Y. Kusuki and M. Miyaji, “Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block,” JHEP
Original
1905
Earlier work this paper cites.
S. Pal and Z. Sun, “Tauberian-Cardy formula with spin,” JHEP
Original
1910
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
J.-F. Fortin, W. Ma, and W. Skiba, “Higher-Point Conformal Blocks in the Comb Channel,” JHEP
Original
1911
Earlier work this paper cites.
S. Collier, A. Maloney, H. Maxfield, and I. Tsiares, “Universal dynamics of heavy operators in CFT 2
Original
1912
Earlier work this paper cites.
S. Ferrara, A. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory,” Nucl. Phys. B
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE,” Commun. Math. Phys
1984
Earlier work this paper cites.
J. L. Cardy, “Operator content of two-dimensional conformally invariant theories,” Nucl. phys. B
1986
Earlier work this paper cites.
M. Abramowitz, I. A. Stegun, and R. H. Romer, “Handbook of mathematical functions with formulas, graphs, and mathematical tables,” 1988
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Polynomial Equations for Rational Conformal Field Theories,” Phys. Lett. B
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
J. L. Cardy, “Operator content and modular properties of higher dimensional conformal field theories,” Nucl. Phys. B
1991
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Physical review e
1994
Earlier work this paper cites.
B. Ponsot and J. Teschner, “Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R)),” Commun. Math. Phys
2001
Earlier work this paper cites.
J. Pollack, M. Rozali, J. Sully, and D. Wakeham, “Eigenstate Thermalization and Disorder Averaging in Gravity,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
B. Mukhametzhanov and S. Pal, “Beurling-Selberg Extremization and Modular Bootstrap at High Energies,” SciPost Phys
Original
2003
Earlier work this paper cites.
J.-F. Fortin, W.-J. Ma, and W. Skiba, “Six-point conformal blocks in the snowflake channel,” JHEP
Original
2004
Earlier work this paper cites.
T. Anous and F. M. Haehl, “On the Virasoro six-point identity block and chaos,” JHEP
Original
2005
Earlier work this paper cites.
A. Belin and J. de Boer, “Random statistics of OPE coefficients and Euclidean wormholes,” Class. Quant. Grav
Original
2006
Earlier work this paper cites.

Similar

A. Blommaert, “Dissecting the ensemble in JT gravity,” arXiv:2006.13971 [hep-th]
Original
2006
Cited alongside, same era.
J. Richter, A. Dymarsky, R. Steinigeweg, and J. Gemmer, “Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies,” Phys. Rev. E
Original
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Cited alongside, same era.
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Original
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Original
2008
Cited alongside, same era.
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Then

D. Das, S. Datta, and S. Pal, “Universal asymptotics of three-point coefficients from elliptic representation of Virasoro blocks,” Phys. Rev. D
Original
2018
Later among the works it cites.
E. M. Brehm, D. Das, and S. Datta, “Probing thermality beyond the diagonal,” Phys. Rev. D
Original
2018
Later among the works it cites.
A. Romero-Bermúdez, P. Sabella-Garnier, and K. Schalm, “A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled,” JHEP
Original
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Later among the works it cites.
Y. Hikida, Y. Kusuki, and T. Takayanagi, “Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories,” Phys. Rev. D
Original
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Later among the works it cites.
F. M. Haehl and M. Rozali, “Fine Grained Chaos in A d S 2 AdS_{2} Gravity,” Phys. Rev. Lett

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2021

OPE statistics from higher-point crossing

Anous, Tarek, Belin, Alexandre, de Boer, Jan et al.

Understand

We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories.

These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions.
They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients.
We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension.

Built on

T. Anous and J. Sonner, “Phases of scrambling in eigenstates,” SciPost Phys
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, “Modular invariance, tauberian theorems and microcanonical entropy,” JHEP
Original
1904
Earlier work this paper cites.
Y. Kusuki and M. Miyaji, “Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block,” JHEP
Original
1905
Earlier work this paper cites.
S. Pal and Z. Sun, “Tauberian-Cardy formula with spin,” JHEP
Original
1910
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
J.-F. Fortin, W. Ma, and W. Skiba, “Higher-Point Conformal Blocks in the Comb Channel,” JHEP
Original
1911
Earlier work this paper cites.
S. Collier, A. Maloney, H. Maxfield, and I. Tsiares, “Universal dynamics of heavy operators in CFT 2
Original
1912
Earlier work this paper cites.
S. Ferrara, A. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory,” Nucl. Phys. B
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE,” Commun. Math. Phys
1984
Earlier work this paper cites.
J. L. Cardy, “Operator content of two-dimensional conformally invariant theories,” Nucl. phys. B
1986
Earlier work this paper cites.
M. Abramowitz, I. A. Stegun, and R. H. Romer, “Handbook of mathematical functions with formulas, graphs, and mathematical tables,” 1988
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Polynomial Equations for Rational Conformal Field Theories,” Phys. Lett. B
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
J. L. Cardy, “Operator content and modular properties of higher dimensional conformal field theories,” Nucl. Phys. B
1991
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Physical review e
1994
Earlier work this paper cites.
B. Ponsot and J. Teschner, “Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R)),” Commun. Math. Phys
2001
Earlier work this paper cites.
J. Pollack, M. Rozali, J. Sully, and D. Wakeham, “Eigenstate Thermalization and Disorder Averaging in Gravity,” Phys. Rev. Lett
Original
2002
Earlier work this paper cites.
B. Mukhametzhanov and S. Pal, “Beurling-Selberg Extremization and Modular Bootstrap at High Energies,” SciPost Phys
Original
2003
Earlier work this paper cites.
J.-F. Fortin, W.-J. Ma, and W. Skiba, “Six-point conformal blocks in the snowflake channel,” JHEP
Original
2004
Earlier work this paper cites.
T. Anous and F. M. Haehl, “On the Virasoro six-point identity block and chaos,” JHEP
Original
2005
Earlier work this paper cites.
A. Belin and J. de Boer, “Random statistics of OPE coefficients and Euclidean wormholes,” Class. Quant. Grav
Original
2006
Earlier work this paper cites.

Similar

A. Blommaert, “Dissecting the ensemble in JT gravity,” arXiv:2006.13971 [hep-th]
Original
2006
Cited alongside, same era.
J. Richter, A. Dymarsky, R. Steinigeweg, and J. Gemmer, “Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies,” Phys. Rev. E
Original
2007
Cited alongside, same era.
S. Caron-Huot, Y. Gobeil, and Z. Zahraee, “The leading trajectory in the 2+1D Ising CFT,” arXiv:2007.11647 [hep-th]
Original
2007
Cited alongside, same era.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Cited alongside, same era.
C. Bercini, V. Gonçalves, and P. Vieira, “Light-Cone Bootstrap of Higher Point Functions and Wilson Loop Duality,” Phys. Rev. Lett

Then

D. Das, S. Datta, and S. Pal, “Universal asymptotics of three-point coefficients from elliptic representation of Virasoro blocks,” Phys. Rev. D
Original
2018
Later among the works it cites.
E. M. Brehm, D. Das, and S. Datta, “Probing thermality beyond the diagonal,” Phys. Rev. D
Original
2018
Later among the works it cites.
A. Romero-Bermúdez, P. Sabella-Garnier, and K. Schalm, “A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled,” JHEP
Original
2018
Later among the works it cites.
Y. Hikida, Y. Kusuki, and T. Takayanagi, “Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories,” Phys. Rev. D
Original
2018
Later among the works it cites.
F. M. Haehl and M. Rozali, “Fine Grained Chaos in A d S 2 AdS_{2} Gravity,” Phys. Rev. Lett

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2008

Cited alongside, same era.

D. Stanford, “More quantum noise from wormholes,” arXiv:2008.08570 [hep-th]

Original

2008

Cited alongside, same era.

L. Hadasz, Z. Jaskolski, and P. Suchanek, “Recursive representation of the torus 1-point conformal block,” JHEP

Original

2010

Cited alongside, same era.

A. M. García-García and V. Godet, “Euclidean wormhole in the Sachdev-Ye-Kitaev model,” Phys. Rev. D

Original

2010

Cited alongside, same era.

S. Hellerman, “A Universal Inequality for CFT and Quantum Gravity,” JHEP

Original

2011

Cited alongside, same era.

D. Das, Y. Kusuki, and S. Pal, “Universality in asymptotic bounds and its saturation in 2 2 D CFT,” JHEP

Original

2011

Cited alongside, same era.

D. Pappadopulo, S. Rychkov, J. Espin, and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev. D

Original

2012

Cited alongside, same era.

A. Belin, J. De Boer, P. Nayak, and J. Sonner, “Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity,” arXiv:2012.07875 [hep-th]

Original

2012

Cited alongside, same era.

Original

2018