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

Authors: Chris Hull and Ulf Lindström Preprint number UUITP-20/17 Off-shell $(4,0)$ supermultiplets in  2-dimensions are constructed. 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 the 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.