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 (K3 × T2WP1122612) 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 permutes the different singularity loci of the moduli of WP1122612. We study the transformation under S-duality of the Calabi-Yau Yukawa couplings.