VANISHING THEOREMS FOR THE SELF-DUAL N=2 STRING

It is proven that up to possible surface terms, the only non-vanishing momentum-dependent amplitudes for the self-dual N = 2 string in R(2,2 ) the tree-level two and three-point functions, and the only non-vanis hing momentum-independent amplitudes are the one-loop partition functi on and the tree-level two and four-point functions. The calculations a re performed using the topological prescription developed in an earlie r paper with Vafa. As in supersymmetric non-renormalization theorems, the vanishing proof is based on a relationship between the zero-moment um dilaton and axion.