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On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation

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arxiv hep-th/0508019 v3 pith:OLTXWFR2 submitted 2005-08-03 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords equationfunctionknizhnik-zamolodchikovflowrepresentationsolutionsspectralsymmetry
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It is well known that five-point function in Liouville field theory provides a representation of solutions of the SL(2,R)_k Knizhnik-Zamolodchikov equation at the level of four-point function. Here, we make use of such representation to study some aspects of the spectral flow symmetry of sl(2)_k affine algebra and its action on the observables of the WZNW theory. To illustrate the usefulness of this method we rederive the three-point function that violates the winding number in SL(2,R) in a very succinct way. In addition, we prove several identities holding between exact solutions of the Knizhnik-Zamolodchikov equation.

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    This paper verifies, at second order in conformal perturbation theory, that the proposed marginal deformation of a symmetric orbifold CFT reproduces the residues of three-point superstring correlators on AdS3 x S3 x T4.

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