Conformal blocks for admissible representations of $SL(2)$ current algebra

Details Conformal blocks for admissible representations of $SL(2)$ current algebra Conformal blocks for admissible representations of $SL(2)$ current algebra

1995-10-10

arxiv.org/abs/hep-th/9510059v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX

Scientific paper

A review is presented of the recently obtained expressions for conformal blocks for {\it admissible} representations in $SL(2)$ current algebra based on the Wakimoto free field construction. In this realization one needs to introduce a second screening charge, one which depends on fractional powers of free fields. The techniques necessary to deal with these complications are developed, and explicit general integral representations for conformal blocks on the sphere are provided. The fusion rules are discussed and as a check it is verified that the conformal blocks satisfy the Knizhnik-Zamolodchikov equations. (Talk presented by J. Rasmussen at the Leuven workshop, July 10-14 1995, to appear in the proceedings)

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