On holomorphic factorization for free conformal fields

Abstract

For free spin j conformal fields on a compact Riemann surface without boundary, we prove, locally over the space of complex structures - parametrized by Beltrami differentials - the existence of a class of partition functions which are holomorphically factorized, and whose diffeomorphism anomalies split holomorphically. For a collection of such models with vanishing total central charge, one recovers the Belavin-Knizhnik theorem.