N=4 TOPOLOGICAL STRINGS

We show how to make a topological string theory starting from an N = 4 superconformal theory. The critical dimension for this theory is c ($) over cap = 2 (c = 6). It is shown that superstrings (in both the RNS and GS formulations) and critical N = 2 strings are special cases of this topological theory. Applications for this new topological theory include: (1) Proving the vanishing to all orders of all scattering amplitudes for the self-dual N = 2 string with flat background, with the exception of the three-point function and the closed-string partition function; (2) Showing that the topological partition function of the N = 2 string on the K3 background may be interpreted as computing the superpotential in harmonic superspace generated upon compactification of type II superstrings from 10 to 6 dimensions; and (3) Providing a new prescription for calculating superstring amplitudes which appears to be free of total-derivative ambiguities.