Elliptic Wess-Zumino-Witten model from elliptic Chern-Simons theory

This Letter continues the program aimed at analysing of the scalar product of states in the Chem-Simons theory. It treats the elliptic case with group SU2. 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.