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Integral representation of solutions of the elliptic Knizhnik--Zamolodchikov--Bernard equations

Giovanni Felder·Alexander Varchenko
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Abstract

We give an integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations for arbitrary simple Lie algebras. If the level is a positive integer, we obtain formulas for conformal blocks of the WZW model on a torus. The asymptotics of our solutions at critical level gives eigenfunctions of Euler-Calogero-Moser integrable $N$-body systems. As a by-product, we obtain some remarkable integral identities involving classical theta functions.

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Giovanni Felder, Alexander Varchenko. 1995-05-19. Integral representation of solutions of the elliptic Knizhnik--Zamolodchikov--Bernard equations. https://arxiv.org/abs/hep-th/9502165

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