On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation

Details On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation

2005-08-03

arxiv.org/abs/hep-th/0508019v3

Phys.Lett. B628 (2005) 148-156

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, no figures. v2: Typos corrected, formula and references added. v3: typo corrected in equation (20)

Scientific paper

10.1016/j.physletb.2005.09.031

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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