New N=2 matter couplings in superspace

The generalized N = 2 tensor multiples are defined and the corresponding interacting models are constructed in N = 2 superspace in four dimensions. The couplings with the N = 2 Yang-Mills fields are given. The two-dimensional nonlinear N = 4 supersymmetric sigma models obtained via dimensional reduction are known to be finite. The construction gives rise to a variety of explicitly constructed quaternionic-Kahler metrics. Some two-dimensional N = 4 supersymmetric sigma models with nonvanishing torsion turn out to be equivalent to the ordinary N = 4 hyper-Kahler nonlinear sigma models without torsion