Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
arXiv:hep-th/9502161 · doi:10.1007/BF00398317
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.
18 pages, latex
References in corpus (7)
- Gaudin Model, Bethe Ansatz and Critical Level
- Quasiclassical asymptotics of solutions to the KZ equations
- Off-Shell Bethe Ansatz Equation and N-point Correlators in the SU(2) WZNW Theory
- Chern-Simons States at Genus One
- On the affine analogue of Jack's and Macdonald's polynomials
- SU(2) WZW Theory at Higher Genera
- Coulomb Gas Representation of the SU(2) WZW Correlators at Higher Genera