Thermal Conformal Blocks

TL;DR

This paper analyzes thermal conformal blocks in general-dimensional conformal field theories, providing analytic formulas and asymptotic results for operator coefficients, with connections to AdS Witten diagrams.

Contribution

It offers an analytic expression for scalar thermal conformal blocks and derives asymptotic formulas for three-point coefficients involving heavy operators.

Findings

Derived integral representations related to AdS Witten diagrams

Provided an explicit hypergeometric function formula for scalar blocks

Obtained asymptotic behavior of three-point coefficients for heavy operators

Abstract

We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations related to AdS Witten diagrams. We give an analytic formula for the scalar conformal block in terms of generalized hypergeometric functions. As an application, we deduce an asymptotic formula for the three-point coeffcients of primary operators in the limit where two of the operators are heavy.