Off-shell superconformal nonlinear sigma-models in three dimensions

TL;DR

This paper develops superspace methods to construct and analyze off-shell superconformal sigma-models in three dimensions with extended supersymmetry, revealing new insights into their structure and symmetries.

Contribution

It introduces superspace techniques for off-shell N=1,2,3,4 superconformal sigma-models and proves that N=3 supersymmetry implies N=4 in both on-shell and off-shell frameworks.

Findings

Constructed general off-shell superconformal sigma-models in 3D.

Proved N=3 supersymmetry implies N=4 in superspace.

Explored supertwistor realizations of supermanifolds.

Abstract

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies 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 N-extended superconformal groups act transitively and which include Minkowski space as a subspace.