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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.
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J. Teschner, The mini-superspace limit of the SL(2, ℂ {\mathbb{C}} )/SU(2) WZNW model
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A. V. Stoyanovsky, A relation between the Knizhnik–Zamolodchikov and Belavin–Polyakov–Zamolodchikov systems of partial differential equations
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K. Hosomichi and S. Ribault, Solution of the H 3 + H^{+}_{3} model on a disc
2007
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