Differential Equations Associated to The SU(2) WZNW Model on Elliptic Curves

Details Differential Equations Associated to The SU(2) WZNW Model on Elliptic Curves Differential Equations Associated to The SU(2) WZNW Model on Elliptic Curves

1994-12-26

arxiv.org/abs/hep-th/9412219v2

Publ.Res.Inst.Math.Sci.Kyoto 32 (1996) 207-233

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, AMS-Tex Version 2.1, no figures

Scientific paper

We study the $SU(2)$ WZNW model over a family of elliptic curves. Starting from the formulation developed by Tsuchiya, Ueno and Yamada, we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard equations. Our system completely determines the $N$-point functions and it is regarded as a natural elliptic analogue of the one developed by Tsuchiya and Kanie for the projective line. We also calculate the system for the 1-point functions explicitly. This gives a generalization of the system for $\hat\frak{sl}(2,\C)$-characters derived by Eguchi and Ooguri.

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