CFTs on Riemann surfaces of genus g ≥ 1

Abstract

The purpose of this thesis is to argue that N-point functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2-point function of the Virasoro field on hyperelliptic Riemann surfaces of genus g≥ 1. N-point functions for higher N are obtained inductively, and we show that they have a nice graphical representation. We discuss the Virasoro 3-point function with application to the Virasoro (2,5) minimal model.