Superconformal Sigma Models in Three Dimensions

TL;DR

This paper constructs superconformal sigma models in three dimensions with extended supersymmetry, exploring their geometric structures, symmetries, and connections to supergravity, especially for N ≤ 4.

Contribution

It provides explicit constructions of superconformal gauged sigma models with N=1,2 in three dimensions, detailing their geometric targets and symmetry properties, and links them to supergravity frameworks.

Findings

Models with N>4 have flat targets.

Models with N ≤ 4 have cone-shaped targets with Sasakian bases.

Superconformal symmetry requires conformal Killing spinors in spacetime.

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 \leq 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 Poincare supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N \geq 2.