S-duality and supersymmetry on curved manifolds

Abstract

We perform a systematic study of S-duality for $\mathcal{N}=2$ 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.

51 pages

References in corpus (2)

• S-duality as a beta-deformed Fourier transform
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories

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