Off-shell superconformal nonlinear sigma-models in three dimensions

Abstract

We develop superspace techniques to construct general off-shell \( \mathcal{N} \leq 4 \) super-conformal sigma-models in three space-time dimensions. The most general \( \mathcal{N} = 3 \) and \( \mathcal{N} = 4 \) superconformal sigma-models are constructed in terms of \( \mathcal{N} = 2 \) chiral superfields. Several superspace proofs of the folklore statement that \( \mathcal{N} = 3 \) supersymmetry implies \( \mathcal{N} = 4 \) are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional \( \mathcal{N} \)-extended superconformal groups act transitively and which include Minkowski space as a subspace.