S-duality and the Calabi-Yau interpretation of the N=4 to N=2 flow

Abstract

The action of the S-duality Sl(2,Z) group on the moduli of the Calabi-Yau manifold WIP^(12)_(11226) appearing in the rank two dual pair (K3 × T 2/WIP^(12)_(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 WIP^(12)_(11226). We study the transformation under S-duality of the Calabi-Yau Yukawa couplings.