TOPOLOGICAL AMPLITUDES IN HETEROTIC SUPERSTRING THEORY

We show that certain heterotic string amplitudes are given in terms of correlators of the twisted topological (2,0) SCFT, corresponding to t he internal sector of the N = 1 space-time supersymmetric background. The genus g topological partition function Fg corresponds to a term in the effective action of the form W-2g, where W is the gauge or gravit ational superfield. We study also recursion relations related to holom orphic anomalies, showing that, contrary to the type II case, they inv olve correlators of anti-chiral superfields. The corresponding terms i n the effective action are of the form W(2g)Pi(n), where Pi is a chira l superfield obtained by chiral projection of a general superfield. We observe that the structure of the recursion relations is that of N = 1 spacetime supersymmetry Ward identity. We give also a solution of th e tree-level recursion relations and discuss orbifold examples.