N = (4,4) Supersymmetry and T-Duality

A sigma model with four-dimensional target space parametrized by chiral and twisted chiral N =(2, 2) superfields can be extended to N =(4, 4) supersymmetry off-shell, but this is not true for a model of semichiral fields, where the N = (4, 4) supersymmetry can only be realized on-shell. The two models can be related to each other by T-duality. In this paper we perform a duality transformation from a chiral and twisted chiral model with off-shell N = (4, 4) supersymmetry to a semichiral model. We find that additional non-linear terms must be added to the original transformations to obtain a semichiral model with N =(4, 4) supersymmetry, and that the algebra closes on-shell as a direct consequence of the T-duality.