Gauge-invariant sigma models in N=2 superspace

We construct a new broad class of gauge-invariant nonlinear sigma models in N=2 superspace. The dimensional reduction of the theories obtained to d=2 leads to N=4 nonlinear sigma models which are devoid of ultraviolet divergence in all orders of perturbation theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1989.