Superconformal sigma models in three dimensions

Abstract

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N > 4 have necessarily flat targets, but the models with N ⩽ 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three-dimensional spacetimes admit conformal Killing spinors which we examine in detail. We present explicit results for the gauged superconformal theories for N = 1 , 2 . In particular, we gauge a suitable subgroup of the isometry group of the cone in a superconformal way. We finally show how these sigma models can be obtained from Poincaré supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N ⩾ 2 .