Operator product expansion in SL(2) conformal field theory

TL;DR

This paper investigates the operator product expansion in SL(2) conformal field theories, focusing on primary fields and their correlators, and highlights the role of degenerate representations in obtaining correct OPEs.

Contribution

It provides a detailed analysis of primary fields and their correlators in SL(2) CFTs, clarifying the conditions for correct OPEs involving degenerate representations.

Findings

Correct OPE obtained with degenerate highest weight primary fields

Explicit calculation of two- and three-point functions

Insights into OPE structure in SL(2,R) WZNW model

Abstract

In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL(2,R) WZNW model.