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 WP1122612 appearing in the rank-two dual pair (K-3 x T-2 /WP1122612) is defined by interpreting the N = 4 to N = 2 flow, for SU (2) supersymmetric Yang-Mills, 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 permut es the different singularity loci of the moduli of WP1122612. We study the transformation under S-duality of the Calabi-Yau Yukawa couplings .