The Wess-Zumino-Witten models on the N-punctured Riemann sphere

Abstract

WZW models on the N-punctured Riemann sphere S 2 are discussed. The Ward identities are derived. According to the Riemann-Roch theorem, we construct a basis of meromorphic λ differentials. The expanding coefficients of the stress-energy tensor and currents are expressed by the meromorphic λ=−1 and λ=0 differentials. Thus multi-pole Virasoro and Kac-Moody algebras are obtained. A highest-weight representation of the combined multi-pole Kac-Moody and Virasoro algebra is generated.