Twisted multiplets and new supersymmetric non-linear σ-models

A new D = 2 supersymmetric representation, the twisted chiral multiplet, is derived. Describing spins zero and one-half, the twisted multiplet is used to formulate supersymmetric nonlinear σ-models with N = 2,4 extended supersymmetry. In general, the geometries of these new theories fall outside the classification given by Alvarez-Gaumé and Freedman. We give a complete description of the geometry of these new models; the scalar manifolds are not Kähler but are hermitian locally product spaces.