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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.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan

    Katsuhisa Mimachi

  2. Department of Mathematics, Kyushu University, Ropponmatsu, Fukuoka, 810-8560, Japan

    Masaaki Yoshida

Authors
  1. Katsuhisa Mimachi
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  2. Masaaki Yoshida
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Correspondence to Katsuhisa Mimachi.

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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.

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Mimachi, K., Yoshida, M. Intersection Numbers of Twisted Cycles Associated with the Selberg Integral and an Application to the Conformal Field Theory. Commun. Math. Phys. 250, 23–45 (2004). https://doi.org/10.1007/s00220-004-1138-z

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  • DOI: https://doi.org/10.1007/s00220-004-1138-z

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