TWISTER SPACES FOR HYPER-KAHLER MANIFOLDS WITH TORSION

We construct the twister space associated with an HKT manifold, that i s, a hyper-Kahler manifold with torsion, a type of geometry that arise s as the target space geometry in two-dimensional sigma models with (4 ,0) supersymmetry. We show that this twister space has a natural compl ex structure and is a holomorphic fibre bundle over the complex projec tive line with fibre me associated HKT manifold. We also show how the metric and torsion of the HKT manifold can he determined from data on the twister space by a reconstruction theorem. We give a geometric des cription of the sigma model (4,0) superfields as holomorphic maps (sui tably understood) from a twistorial extension of (4,0) superspace (har monic superspace) into the twister space of the sigma model target man ifold and write an action for the sigma model in terms of these (4,0) superfields.