H^+_3 WZNW model from Liouville field theory

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Hikida, Yasuaki
Schomerus, Volker
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Abstract
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There exists an intriguing relation between genus zero correlation functions in the H^+_3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program.
Comment: 33 pages, no figure, minor changes, several equations corrected
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High Energy Physics - Theory
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