Hyper–Kähler sigma models in extended superspace

Self-interacting theories for generalized tensor multiplets and relaxed hypermultiplet of matter are constructed in $N=2, \ d=4$ superspace. Explicit formulation of a large set of new two-dimensional $N=4$ sigma-models with the hyper-Kähler metrics is given. It is shown that ultra-violet divergences in these theories cancel in all orders of perturbation theory.