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

Abstract

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.

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

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• The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation
• Solution of the H3+ model on a disc
• Branes in the OSP(1|2) WZNW model
• Two AdS2 branes in the Euclidean AdS3
• A localising AdS${}_3$ sigma model
• Are there really any AdS_2 branes in the euclidean (or not) AdS_3?
• Zamolodchikov operator-valued relations for SL(2,R)_k WZNW model
• Liouville theory and logarithmic solutions to Knizhnik-Zamolodchikov equation
• String correlators on ${\text{AdS}}_3$: Four-point functions
• A Note on Z_2 Symmetries of the KZ Equation
• AdS2 D-branes in AdS3 spacetime
• Notes on the SL(2,R) CFT
• On the Various Types of D-Branes in the Boundary H3+ Model
• On Factorization Constraints for Branes in the H3+ Model