SU(2) WZW Theory at Higher Genera

Details SU(2) WZW Theory at Higher Genera SU(2) WZW Theory at Higher Genera

1994-02-16

arxiv.org/abs/hep-th/9402091v1

Commun.Math.Phys. 169 (1995) 329-372

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, IHES/P/94/10, Latex file

Scientific paper

10.1007/BF02099476

We compute, by free field techniques, the scalar product of the SU(2) Chern-Simons states on genus > 1 surfaces. The result is a finite-dimensional integral over positions of ``screening charges'' and one complex modular parameter. It uses an effective description of the CS states closely related to the one worked out by Bertram. The scalar product formula allows to express the higher genus partition functions of the WZW conformal field theory by finite-dimensional integrals. It should provide the hermitian metric preserved by the Knizhnik-Zamolodchikov-Bernard connection describing the variations of the CS states under the change of the complex structure of the surface.

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