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In this review article we describe the localization of three dimensional= 2 N supersymmetric
theories on compact manifolds, including the squashed sphere, Sb 3, the lens space, Sb p …

We present a uniform treatment of rigid supersymmetric field theories in a curved
spacetime\(\mathcal {M}\), focusing on four-dimensional theories with four supercharges …

We study the N= 2 four-dimensional superconformal index in various interesting limits, such
that only states annihilated by more than one supercharge contribute. Extrapolating from the …

A bstract Many examples of low-energy dualities have been found in supersymmetric gauge
theories with four supercharges, both in four and in three space-time dimensions. In these …

A bstract We construct supersymmetric field theories on Riemannian three-
manifolds\(\mathcal {M}\), focusing on\(\mathcal {N}\)= 2 theories with a U (1) R symmetry …

A bstract The analytic properties of the\(\mathcal {N}= 2\) superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of …

A bstract We consider three-dimensional\(\mathcal {N}= 2\) superconformal field theories on
a threesphere and analyze their free energy F as a function of background gauge and …

A bstract We systematically analyze Riemannian manifolds\(\mathcal {M}\) that admit rigid
supersymmetry, focusing on four-dimensional\(\mathcal {N}={1}\) theories with a U (1) R …

A bstract We present a set of equations for a 4D Killing spinor which guarantees the Seiberg-
Witten theories on a curved background to be supersymmetric. The equations involve an SU …