Coulomb-gas representation on higher-genus surfaces

In this paper we use the Coulomb-gas approach to construct the minimal-model conformal blocks of higher-genus Riemann surfaces. We define the higher-genus blocks by sewing, and write them in terms of the rational blocks of a compactified scalar field. We show that spurious states decouple, which implies that the blocks degenerate correctly. As an example, we compute the genus-two partition function, and verify modular invariance for the subset of minimal models which only require one type of screening charge.