Confluent primary fields in the conformal field theory

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 sl(2), 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 sl(2), these differential operators are the same as those of the confluent KZ equations (Jimbo et al 2008).