STRING THEORY NEAR A CONIFOLD SINGULARITY

We demonstrate that type II string theory compactified on a singular C alabi-Yau manifold is related to c = 1 string theory compactified at t he self-dual radius. We establish this result in two ways. First we sh ow that complex structure deformations of the conifold correspond, on the mirror manifold, to the problem of maps from two dimensional surfa ces to S-2. Using two dimensional QCD we show that this problem is ide ntical to c = 1 string theory. We then give an alternative derivation of this correspondence by mapping the theory of complex structure defo rmations of the conifold to Chem-Simons theory on s(3). These results, in conjunction with similar results obtained for the compactification of the heterotic string on K-3 X T-2, provide strong evidence in favo ur of S-duality between type II strings compactified on a Calabi-Yau m anifold and the heterotic string on K-3 X T-2.