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arXiv · hep-th/9411004

Conformal blocks on elliptic curves and the Knizhnik--Zamolodchikov--Bernard equations

Giovanni Felder·Christian Wieczerkowski
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Abstract

We give an explicit description of the vector bundle of WZW conformal blocks on elliptic curves with marked points as subbundle of a vector bundle of Weyl group invariant vector valued theta functions on a Cartan subalgebra. We give a partly conjectural characterization of this subbundle in terms of certain vanishing conditions on affine hyperplanes. In some cases, explicit calculation are possible and confirm the conjecture. The Friedan--Shenker flat connection is calculated, and it is shown that horizontal sections are solutions of Bernard's generalization of the Knizhnik--Zamolodchikov equation.

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Giovanni Felder, Christian Wieczerkowski. 1994-11-01. Conformal blocks on elliptic curves and the Knizhnik--Zamolodchikov--Bernard equations. https://doi.org/10.1007/bf02099366

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