Superconformal structures on the three-sphere

Understand

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3.

• Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived.
• We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) 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}.