Universal dynamics of heavy operators in CFT2

被引:63
作者
Collier, Scott [1 ]
Maloney, Alexander [2 ]
Maxfield, Henry [3 ]
Tsiares, Ioannis [2 ]
机构
[1] Harvard Univ, Jefferson Phys Lab, Cambridge, MA 02138 USA
[2] McGill Univ, Dept Phys, Montreal, PQ H3A 2T8, Canada
[3] Univ Calif Santa Barbara, Dept Phys, Santa Barbara, CA 93106 USA
基金
加拿大自然科学与工程研究理事会;
关键词
AdS-CFT Correspondence; Conformal Field Theory; CONFORMAL SYMMETRY; BOOTSTRAP;
D O I
10.1007/JHEP07(2020)074
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
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 CFT2 structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving crossing kernels for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the conformal blocks. The higher genus modular kernels are obtained by sewing together the elementary kernels for four-point crossing and modular transforms of torus one-point functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics of heavy operators in any CFT. The large central charge limit provides a link with 3D gravity, where the averaging over heavy states corresponds to a coarse-graining over black hole microstates in holographic theories. Our formula also provides an improved understanding of the Eigenstate Thermalization Hypothesis (ETH) in CFT2, and suggests that ETH can be generalized to other kinematic regimes in two dimensional CFTs.
引用
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页数:59
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