SUPERSYMMETRY AND KAHLER MANIFOLDS

We give the supersymmetric extension of non-linear models with scalar fields taking values in a complex Kähler manifold. The supersymmetry is simple for four-dimensional Minkowski space, complex for two-dimensional space-time. The supersymmetric symmetric lagrangian is given by a simple and elegant formula in terms of the Kähler metric of the manifold. (Anti-) self- dual supersymmetric solutions are also given. The special cases of the CPn-1 models and of models with scalar fields valued in a Grassman manifold Gp,q=G(p+q)/G(p) ⊗ U(q) are discussed in some detail. © 1979.