Communications in Mathematical Physics

, Volume 250, Issue 1, pp 23–45

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


DOI: 10.1007/s00220-004-1138-z

Cite this article as:
Mimachi, K. & Yoshida, M. Commun. Math. Phys. (2004) 250: 23. doi:10.1007/s00220-004-1138-z


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of MathematicsKyushu UniversityFukuokaJapan