On holomorphic factorization of WZW and coset models (Q1189218)

In the WZW model of the 2-dimensional conformal field theory a two- dimensional surface \(\Sigma\) (a world sheet) is moving in a group manifold \(G\) with the usual action as an integral over \(\Sigma\) of an invariant form on the Lie algebra of \(G\), augmented by the so-called Wess-Zumino term, which is an integral over a 3-manifold \(B\) (with \(\partial B=\Sigma\)) of an invariant 3 form \(\omega\) on \(G\). This model is essentially exactly soluble due to conformal invariance. The partition function \(Z\) is defined by the usual path integral and depends only on the complex structure determined by the metric \(\delta\) on \(\Sigma\). The solvability stems from holomorphic factorization which is discussed in detail in this paper.