Three-point functions and operator product expansion in the SL(2) conformal field theory

TL;DR

This paper derives explicit formulas for three-point functions in SL(2) conformal field theory and discusses the operator product expansion, aligning it with SL(2,R) representation tensor products.

Contribution

It provides the first explicit analytic expressions for three-point functions in SL(2) CFT and proposes an OPE prescription consistent with SL(2,R) representation theory.

Findings

Explicit three-point function formulas for primary fields.

A new OPE prescription matching SL(2,R) tensor products.

Consistency with classical representation limits.

Abstract

In the SL(2) conformal field theory, we write down and analyze the analytic expression of the three-point functions of generic primary fields with definite SL(2) weights. Using these results, we discuss the operator product expansion in the SL(2,R) WZW model. We propose a prescription of the OPE, the classical limit of which is in precise agreement with the tensor products of the representations of SL(2,R).