Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
High Energy Physics - Theory
2016-09-06 v1
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.
Keywords
Cite
@article{arxiv.hep-th/9502161,
title = {Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory},
author = {Fernando Falceto and Krzysztof Gawedzki},
journal= {arXiv preprint arXiv:hep-th/9502161},
year = {2016}
}
Comments
18 pages, latex