Coulomb Gas Realization

Abstract

The Ising model correlation functions are too peculiar and too simple to provide a general and efficient method to compute correlation functions of minimal models. It is however known that many models have strong connections with the Coulomb gas in two dimensions. We will explain here a general method which permits to realize any minimal model as a Coulomb gas constrained by a charge placed at infinity. This chapter intends to be an introduction rather than an exhaustive discussion and the amount of necessary field theory knowledge will be kept at the lowest possible level. The purpose of this chapter is to show how to compute any correlation function of minimal models and to give a general formula for the operator product expansion coefficients. The technique was developed in the remarkable papers of VI. Dotsenko and Fateev [109, 110].