Monodromy of solutions of the Knizhnik-Zamolodchikov equation: SL(2,C)/SU(2) WZNW model

Details Monodromy of solutions of the Knizhnik-Zamolodchikov equation: SL(2,C)/SU(2) WZNW model Monodromy of solutions of the Knizhnik-Zamolodchikov equation: SL(2,C)/SU(2) WZNW model

2002-04-10

arxiv.org/abs/hep-th/0204085v3

Nucl.Phys. B642 (2002) 114-138

Physics

High Energy Physics

High Energy Physics - Theory

26 pages.v2: relation to prior works made explicit, many references added, minor typos corrected

Scientific paper

Three explicit and equivalent representations for the monodromy of the conformal blocks in the SL(2,C)/SU(2) WZNW model are proposed in terms of the same quantity computed in Liouville field theory. We show that there are two possible fusion matrices in this model. This is due to the fact that the conformal blocks, being solutions to the Knizhnik-Zamolodchikov equation, have a singularity when the SL(2,C) isospin coordinate x equals the worldsheet variable z. We study the asymptotic behaviour of the conformal block when x goes to z. The obtained relation inserted into a four point correlation function in the SL(2,C)/SU(2) WZNW model gives some expression in terms of two correlation functions in Liouville field theory.

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