A bstract 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 fourpoint crossing and modular transforms of torus onepoint 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 ofmore »
A basis of analytic functionals for CFTs in general dimension
A bstract We develop an analytic approach to the fourpoint crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s  and t channel expansions) can be thought of as a vector equation in an infinitedimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s and tchannel conformal blocks of doubletwist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and CaronHuot.
 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10376821
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 8
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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