GRAVITATIONAL INSTANTONS IN HETEROTIC STRING THEORY - THE H-MAP AND THE MODULI DEFORMATIONS OF (4,4) SUPERCONFORMAL THEORIES

We study the problem of string propagation in a general instanton back ground for the case of the complete heterotic superstring. We define t he concept of generalized hyper-Kahler manifolds and we relate it to ( 4,4) superconformal theories. We propose a generalized h-map construct ion that predicts a universal SU(6) symmetry for the modes of the stri ng excitations moving in an instanton background. We also discuss the role of abstract N = 4 moduli and, applying it to the particular limit case of the solvable SU(2) x R instanton found by Callan et al., we s how that it admits deformations and corresponds to a point in a 16-dim ensional moduli space. The geometrical characterization of the other s paces in the same moduli space remains an open problem.