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 $\mathcal{N}$ = 2 supersymmetry, as well as with $\mathcal{N}$ > 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

Superconformal structures on the three-sphere

With the motivation to develop superconformal field theory on S 3 we introduce a 2 n -extended supersphere S 3|4 n with n =1 2 . . . as a homogeneous space of the three-dimensional Euclidean superconformal group OSp (2 n |2 2) such that its bosonic body is S 3 . Supertwistor and bi-supertwistor realizations of S 3|4 n are derived. We study in detail the n =1 case, which is unique in the sense that the R -symmetry subgroup SO * (2 n ) of the superconformal group is compact only for n =1. In particular, we show that the OSp (2|2 2) transformations preserve the chiral subspace of S 3|4 . Several supercoset realizations of S 3|4 n are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched