Algebraic structure of topological superconformal field theory on Riemann surfaces

The algebraic structure of a topological superconformal field theory on a compact Riemann surface is investigated. The Krichever-Novikov [K-N] global operator formalism is used to obtain anN=4 super K-N algebra on a Riemann surface. Subsequently thisN=4 algebra is shown to posses anN=3 K-N subalgebra. TheN=3 subalgebra is then twisted to derive a topological version of the Krichever-Novikov algebra with a residualN=2 superconformal structure. The BRST charge of the associated topological field theory on the Riemann surface is shown to be genus dependent in this formalism and the global generalization of the BRST derivative conditions are obtained. The complete BRST structure of the theory is explicitly elucidated.