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Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory

Fernando Falceto·Krzysztof Gawedzki
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Abstract

This letter continues the program aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU(2). The formal scalar product is expressed as a multiple finite dimensional integral which, if convergent for every state, provides the space of states with a Hilbert space structure. The convergence is checked for states with a single Wilson line where the integral expressions encode the Bethe-Ansatz solutions of the Lame equation. In relation to the Wess-Zumino-Witten conformal field theory, the scalar product renders unitary the Knizhnik-Zamolodchikov-Bernard connection and gives a pairing between conformal blocks used to obtain the genus one correlation functions.

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Fernando Falceto, Krzysztof Gawedzki. 1995-02-28. Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory. https://doi.org/10.1007/bf00398317

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