All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry

TL;DR

This paper formulates off-shell (4,0) supermultiplets in 2D and constructs sigma models with hyperkähler with torsion target spaces, enabling explicit geometric descriptions via extended superspace.

Contribution

It introduces off-shell (4,0) supermultiplets and constructs sigma models with explicit target space geometries using extended superspace techniques.

Findings

Explicit off-shell (4,0) supermultiplet formulations

Construction of sigma models with hyperkähler with torsion target spaces

Use of extended superspace for explicit geometric actions

Abstract

Off-shell $(4,0)$ supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperk\"ahler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.