Superfield theories on S ³ and their localization

We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid N= 2 supersymmetry, as well as with N>2. The construction is based on a supercoset SU(2|1)/U(1) containing S ³ as the bosonic subspace. We derive an explicit form of SU(2|1)/U(1) supervielbein and covariant derivatives, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace.