Higher-genus characters of two-dimensional conformal field theories

Abstract

The generalized characters of the tow-dimenstonal conformal field theories on the Riemann surfaces of higher genus are constructed. The sewing bootstrap program is perpared to find th conforaml blocks of the higher-genus correlation functions through the factorization properties at the boundary of the moduli space with the guiding help of the modular invariance of the partition function. We construct the higher-genus characters of the cirtical Ising model and the level-one Wess-Zumino-Witten models for the simply laced groups. The goddard-Kent-Olive coset construction is assumed to be realized in the higher-genus representation and is used to obtain the charcters of the level-two SU(2) Wess-Zumino-Written model on the Riemann surface. It is straightforward to find the n-point correlation functions on the Riemann surfac by repeating the pinching procedure of the appropriate zero-and/or nonzero-homology cycles.