, Volume 250, Issue 1, pp 23-45
Date: 27 Jul 2004

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

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Abstract

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.

Communicated by L. Takhtajan
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.