Built on

W. Song and J. Xu, Structure Constants from Modularity in Warped CFT
Original
1903
Earlier work this paper cites.
T. Anous and J. Sonner, Phases of scrambling in eigenstates
Original
1903
Earlier work this paper cites.
A. Dymarsky and K. Pavlenko, Generalized Eigenstate Thermalization Hypothesis in 2D Conformal Field Theories
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, Modular invariance, tauberian theorems and microcanonical entropy
Original
1904
Earlier work this paper cites.
S. Datta, P. Kraus, and B. Michel, Typicality and thermality in 2d CFT
Original
1904
Earlier work this paper cites.
S. Ganguly and S. Pal, Bounds on density of states and spectral gap in CFT 2
Original
1905
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
Original
1905
Earlier work this paper cites.
S. Pal, Bound on asymptotics of magnitude of three point coefficients in 2D CFT
Original
1906
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Light-cone modular bootstrap and pure gravity
Original
1906
Earlier work this paper cites.
H. Maxfield, Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
Original
1906
Earlier work this paper cites.
M. Beken, S. Datta, and P. Kraus, Quantum thermalization and Virasoro symmetry
Original
1907
Earlier work this paper cites.
B. Michel, Universality in the OPE Coefficients of Holographic 2d CFTs
Original
1908
Earlier work this paper cites.
S. Pal and Z. Sun, Tauberian-Cardy formula with spin
Original
1910
Earlier work this paper cites.
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
Original
1910
Earlier work this paper cites.
E. M. Brehm and D. Das, Aspects of the S transformation Bootstrap
Original
1911
Earlier work this paper cites.
A. Ghosh, H. Maxfield, and G. J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories
Original
1912
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory
1984
Earlier work this paper cites.
A. B. Zamolodchikov, CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE
1984
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories
1986
Earlier work this paper cites.
A. B. Zamolodchikov, Conformal symmetry in two-dimensional space: Recursion representation of conformal block
1987
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Polynomial Equations for Rational Conformal Field Theories
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Classical and Quantum Conformal Field Theory
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, LECTURES ON RCFT
1989
Earlier work this paper cites.
L. Alvarez-Gaume, C. Gomez, and G. Sierra, Duality and Quantum Groups
1990
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization
1994
Earlier work this paper cites.
H. Dorn and H. J. Otto, Two and three point functions in Liouville theory
1994
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory
1996
Earlier work this paper cites.
A. Strominger, Black hole entropy from near horizon microstates
1998
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))
2001
Earlier work this paper cites.
J. Teschner, Liouville theory revisited
2001
Earlier work this paper cites.
D. Birmingham, I. Sachs, and S. N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes
2002
Earlier work this paper cites.

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2019

Universal Dynamics of Heavy Operators in CFT$_2$

Collier, Scott, Maloney, Alexander, Maxfield, Henry et al.

Understand

We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with $c>1$.

This formula is valid when one or more of the operators has large dimension or -- in the presence of a twist gap -- has large spin.
Our formula is universal in the sense that it depends only on the central charge and not on any other details of the theory.
This result unifies all previous asymptotic formulas for CFT$_2$ structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance.

Built on

W. Song and J. Xu, Structure Constants from Modularity in Warped CFT
Original
1903
Earlier work this paper cites.
T. Anous and J. Sonner, Phases of scrambling in eigenstates
Original
1903
Earlier work this paper cites.
A. Dymarsky and K. Pavlenko, Generalized Eigenstate Thermalization Hypothesis in 2D Conformal Field Theories
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, Modular invariance, tauberian theorems and microcanonical entropy
Original
1904
Earlier work this paper cites.
S. Datta, P. Kraus, and B. Michel, Typicality and thermality in 2d CFT
Original
1904
Earlier work this paper cites.
S. Ganguly and S. Pal, Bounds on density of states and spectral gap in CFT 2
Original
1905
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
Original
1905
Earlier work this paper cites.
S. Pal, Bound on asymptotics of magnitude of three point coefficients in 2D CFT
Original
1906
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Light-cone modular bootstrap and pure gravity
Original
1906
Earlier work this paper cites.
H. Maxfield, Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
Original
1906
Earlier work this paper cites.
M. Beken, S. Datta, and P. Kraus, Quantum thermalization and Virasoro symmetry
Original
1907
Earlier work this paper cites.
B. Michel, Universality in the OPE Coefficients of Holographic 2d CFTs
Original
1908
Earlier work this paper cites.
S. Pal and Z. Sun, Tauberian-Cardy formula with spin
Original
1910
Earlier work this paper cites.
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
Original
1910
Earlier work this paper cites.
E. M. Brehm and D. Das, Aspects of the S transformation Bootstrap
Original
1911
Earlier work this paper cites.
A. Ghosh, H. Maxfield, and G. J. Turiaci, A universal Schwarzian sector in two-dimensional conformal field theories
Original
1912
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory
1984
Earlier work this paper cites.
A. B. Zamolodchikov, CONFORMAL SYMMETRY IN TWO-DIMENSIONS: AN EXPLICIT RECURRENCE FORMULA FOR THE CONFORMAL PARTIAL WAVE AMPLITUDE
1984
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories
1986
Earlier work this paper cites.
A. B. Zamolodchikov, Conformal symmetry in two-dimensional space: Recursion representation of conformal block
1987
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Polynomial Equations for Rational Conformal Field Theories
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Classical and Quantum Conformal Field Theory
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, LECTURES ON RCFT
1989
Earlier work this paper cites.
L. Alvarez-Gaume, C. Gomez, and G. Sierra, Duality and Quantum Groups
1990
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization
1994
Earlier work this paper cites.
H. Dorn and H. J. Otto, Two and three point functions in Liouville theory
1994
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory
1996
Earlier work this paper cites.
A. Strominger, Black hole entropy from near horizon microstates
1998
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))
2001
Earlier work this paper cites.
J. Teschner, Liouville theory revisited
2001
Earlier work this paper cites.
D. Birmingham, I. Sachs, and S. N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes
2002
Earlier work this paper cites.