S-duality and supersymmetry on curved manifolds

Authors: Guido Festuccia and Maxim Zabzine Preprint number: UUITP-24/20 Abstract:  ​We perform a systematic study of S-duality for N=2 supersymmetric non-linear abelian theories on a curved manifold. Localization can be used to compute certain supersymmetric observables in these theories. We point out that localization and S-duality acting as a Legendre transform are not compatible. For these theories S-duality should be interpreted as Fourier transform and we provide some evidence for this. We also suggest the notion of a coholomological prepotential for an abelian theory that gives the same partition function as a given non-abelian supersymmetric theory.