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

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.

arXiv comment8 pages, LaTeX, article.sty, espcrc2.sty

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• Physical States in G/G Models and 2d Gravity
• Fusion algebra at a rational level and cohomology of nilpotent subalgebras of sl_2
• Reduction of the Knizhnik-Zamolodchikov Equation - a Way of Producing Virasoro Algebra Singular Vectors
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Cited by in corpus (7)

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• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
• Affine Jordan cells, logarithmic correlators, and hamiltonian reduction
• Extended chiral algebras in the SU(2)_0 WZNW model
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity
• Conformal Blocks and Correlators in WZNW Model. I. Genus Zero