Conformal Blocks and Correlators in WZNW Model. I. Genus Zero

Abstract

We consider the free field approach or bosonization technique for the Wess-Zumino-Novikov-Witten model with arbitrary Kac-Moody algebra on Riemann surface of genus zero. This subject was much studied previously, and the paper can be partially taken as a brief survey. The way to obtain well-known Schechtman-Varchenko solutions of the Knizhnik-Zamolodchikov equations as certain correlators in free chiral theory is revisited. This gives rise to simple description of space of the WZNW conformal blocks. The general $N$-point correlators of the model are constructed from the conformal blocks using non-chiral action for free fields perturbed by exactly marginal terms. The method involved generalizes the Dotsenko-Fateev prescription for minimal models. As a consequence of this construction we obtain new integral identities.