Integral and Theta Formulae for Solutions of SlN Knizhnik-Zamolodchikov Equations at Level Zero
Atsushi Nakayashiki
Abstract
The solutions of the slN Knizhnik-Zamolodchikov(KZ) equations at level 0 are studied. We present the integral formula which is obtained as a quasi-classical limit of the integral formula for form factors of the SU(N) invariant Thirring model due to F. Smirnov. A proof is given that those integrals satisfy slN KZ equation of level 0. The relation of the integral formulae with the chiral Szego kernel is clarified. As a consequence the integral formula with the special choice of cycles is rewritten in terms of the Riemann theta functions associated with the ZN curve. This formula gives a generalization of Smirnov's formula for sl2.
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