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.

arXiv comment51 pages

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Cited by in corpus (5)

• Gauge theories on compact toric manifolds
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• The Dark Side of Double-Tensor Multiplets