Confluent primary fields in the conformal field theory

TL;DR

This paper extends the concept of primary fields in conformal field theory to irregular singularities for any complex simple Lie algebra, constructing integral representations of confluent hypergeometric functions and linking them to confluent KZ equations.

Contribution

It generalizes primary fields in WZNW models to irregular singularities and constructs integral representations related to confluent hypergeometric functions for all complex simple Lie algebras.

Findings

Integral representations of confluent hypergeometric functions derived

Differential operators match those of confluent KZ equations for sl(2)

New differential operators appear in operator product expansions

Abstract

For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric functions of confluent type, as expectation values of products of generalized primary fields. In the case of sl(2), these integral representations coincide with solutions to confluent KZ equations. Computing the operator product expansion of the energy-momentum tensor and the generalized primary field, new differential operators appear in the result. In the case of sl(2), these differential operators are the same as those of the confluent KZ equations.