Confluent primary fields in the conformal field theory

Abstract

For any complex simple Lie algebra, we generalize the primary fields in the Wess–Zumino–Novikov–Witten conformal field theory for a case with irregular singularities. We refer to these generalized primary fields as confluent primary fields. We present the screening currents Ward identity, a recursion rule for computing the expectation values of the products of confluent primary fields. In the case of , the expectation values of the products of confluent primary fields are integral formulas of solutions to confluent Knizhnik–Zamolodchikov (KZ) equations given in Jimbo et al (2008 J. Phys. A: Math. Theor. 41 175205). By computing the operator product expansion of the energy–momentum tensor T(z) and the confluent primary fields, we obtain new differential operators. Moreover, in the case of , these differential operators are the same as those of the confluent KZ equations (Jimbo et al 2008).