SYMMETRIES ON THE MODULI SPACE OF (2,2) SUPERSTRING VACUA

Symmetries of the space of (2,2) string vacua for c = 3, 6, 9 are discussed in the context of orbifoldized Landau-Ginzburg theories. A general method for finding the maximal symmetry groups on the moduli space untwisted marginal operators is presented, by studying deformations of superpotentials. We give a complete discussion for the c = 3, 6 untwisted sectors. In particular we find non-abelian symmetry groups on the moduli space of c = 6 which are shown to correspond with automorphism groups of K3 surfaces. All these groups are subgroups of O(20, 4, Z). Some elements of these groups relate small volume target spaces to large ones.