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SU(2) WZW theory at higher genera

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Abstract

We compute, by free field techniques, the scalar product of theSU(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 [1]. 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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  1. C.N.R.S., I.H.E.S., 91440, Bures-sur-Yvette, France

    Krzysztof Gawędzki

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  1. Krzysztof Gawędzki
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Communicated by G. Felder

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Gawędzki, K. SU(2) WZW theory at higher genera. Commun.Math. Phys. 169, 329–371 (1995). https://doi.org/10.1007/BF02099476

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  • DOI: https://doi.org/10.1007/BF02099476

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