Non-Linear Supersymmetric $\sigma$-Models and their Gauging in the Atiyah-Ward Space-Time

Abstract

We present a supersymmetric non-linear $\s$-model built up in the $N=1$ superspace of Atiyah-Ward space-time. A manifold of the Kähler type comes out that is restricted by a particular decomposition of the Kähler potential. The gauging of the $\s$-model isometries is also accomplished in superspace.

15 pages, Latex, no figures