On the Wess-Zumino-Witten models on the torus

Denis Bernard
1988 Nuclear Physics B  
We discuss the Ward identities of the Wess-Zumino-Witten models on Riemann surfaces and point out some ambiguities in the description of the zero modes of the currents. In the case of the torus, we show how to describe them and we write the Ward identities in such a way that they become complete. We examine in detail how the Ward identities are related to the Kubo-Martin-Schwinger condition. As an illustration of this formulation, we present a new proof of the Weyl-Kac character formula. The
more » ... ter formula. The proof essentially relies on the mixed Virasoro × Kac-Moody Ward identities and explains the relation of the heat equation on the group manifold to the Weyl-Kac character formula.
doi:10.1016/0550-3213(88)90217-9 fatcat:l2rnbo2fu5hepf4i3ayqqgpcw4