  We show that certain heterotic string amplitudes are given in terms of
correlators of the twisted topological (2,0) SCFT, corresponding to the
internal sector of the N=1 spacetime supersymmetric background. The genus g
topological partition function $F^g$ corresponds to a term in the effective
action of the form $W^{2g}$, where W is the gauge or gravitational superfield.
We study also recursion relations related to holomorphic anomalies, showing
that, contrary to the type II case, they involve correlators of anti-chiral
superfields. The corresponding terms in the effective action are of the form
$W^{2g}\Pi^n$, where $\Pi$ is a chiral 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 the tree level recursion relations and discuss orbifold examples.
