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Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators

J. L. Petersen·J. Rasmussen·M. Yu
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Abstract

Talk presented by J.L. Petersen at the 29th Symposium Ahrenshop, Buckow August 29-September 2, 1995. A presentation is given of the free field realization relevant to SL(2) WZW theories with a Hilbert space based on admissible representations. It is known that this implies the presence of two screening charges, one involving a fractional power of a free field. We develop the use of fractional calculus for treating in general such cases. We derive explicit integral representations of $N$-point conformal blocks. We show that they satisfy the Knizhnik-Zamolodchikov equations and we prove how they are related to minimal conformal blocks via a formulation of hamiltonian reduction advocated by Furlan, Ganchev, Paunov and Petkova.

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J. L. Petersen, J. Rasmussen, M. Yu. 1995-12-21. Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators. https://doi.org/10.1016/0920-5632(96)00312-x

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