Superconformal structures on the three-sphere

© The Authors. With the motivation to develop superconformal field theory on S³, 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 S³. 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. Several supercoset realizations of S^3|4n are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched.