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

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

1995-02-28

arxiv.org/abs/hep-th/9502165v2

Int. Math. Res. Notices (1995) 221-233

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, AmsLaTex; some misprints were corrected

Scientific paper

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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