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

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

1995-02-28

arxiv.org/abs/hep-th/9502161v1

Lett.Math.Phys. 38 (1996) 155-175

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, latex

Scientific paper

10.1007/BF00398317

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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