All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry

TL;DR

This paper constructs off-shell (4,q) supermultiplets in 2D for q=1,2,4, and uses them to develop sigma models with hyperkähler with torsion target spaces, revealing integrable complex structures and explicit geometric actions.

Contribution

It provides the first explicit off-shell formulations of (4,q) supermultiplets in 2D for q=1,2,4 and constructs sigma models with hyperkähler with torsion geometries.

Findings

Explicit off-shell (4,1), (4,2), and (4,4) supermultiplets constructed.

Sigma models with hyperkähler with torsion target spaces developed.

Extended superspace methods enable explicit geometric action constructions.

Abstract

Off-shell $(4,q)$ supermultiplets in 2-dimensions are constructed for $q=1,2,4$. These are used to construct sigma models whose target spaces are hyperk\"ahler with torsion. The off-shell supersymmetry implies the three complex structures are simultaneously integrable and allows us to construct actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.