Intersection Numbers of Twisted Cycles Associated with the Selberg Integral and an Application to the Conformal Field Theory

Intersection numbers of twisted (or loaded) cycles associated with the Selberg integral are studied. In particular, the self-intersection number of the cycle which is invariant under the action of the symmetric group is expressed by the product of trigonometric functions. This formula reproduces the four-point correlation functions in the conformal field theory calculated by Dotsenko-Fateev in [3]. In our study, a compact non-singular model (Terada model) of the configuration space of n+3 points on the real projective line and a q-analogue of the Chu-Vadermonde formula for the hypergeometric series play a crucial role. Intersection numbers of the corresponding cocycles are also studied.This is a revised version of Intersection numbers of twisted cycles and the correlation functions of the conformal field theory, Kyushu Univ. preprint series 2002-23.