Further remarks on the geometry of two-dimensional non-linear σ-models

Abstract

A class of extended supersymmetric two-dimensional non-linear sigma -models can be formulated in terms of constrained extended superfields. The conditions for these constraints to be linearisable are examined. These conditions involve generalised Nijenhuis tensors and curvature tensors constructed from the complex structures on the target manifold. Off-shell constrained extended superfields are constructed for the Yang-Mills sector of the (2, 0) and (4, 0) models. These superfields will exist provided that certain conditions are satisfied; these conditions are most conveniently expressed in terms of the geometry of fibre bundles. The existence of (4, 0) superfields implies that the general (4, 0) sigma -model with Yang-Mills sector is ultraviolet finite.