S-duality and the Calabi-yau Interpretation of the N = 4 to N = 2 Flow

The action of the S-duality Sl(2, Z) group on the moduli of the Calabi-Yau manifold W IP 11226 appearing in the rank two dual pair (K 3 × T 2/W IP 11226) is defined by interpreting the N =4 to N =2 flow, for SU(2) supersymmetric YangMills, in terms of the Calabi-Yau moduli. The different singularity loci are mapped in a one to one way, and the (N =2 limit/point particle limit) is obtained in both cases by the same type of blow up. Moreover, it is shown that the S-duality group permutes the different singularity loci of the moduli of W IP 11226. We study the transformation under S-duality of the Calabi-Yau Yukawa couplings. Address after January 1996, Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030.