K"ahler Potential for Global Symmetry Breaking in Supersymmetric Theories

We have developed N=1 supersymmetric nonlinear realization methods, which realize global symmetry breaking in N=1 supersymmetric theories. The target space of nonlinear sigma models with a linear model origin is a G^C-orbit, which is a non-compact non-homogeneous K"ahler manifold. We show that, if and only if the orbit is open, it includes a compact homogeneous K"ahler manifold as a submanifold, and a class of strictly G-invariant K"ahler potentials reduces to a K"ahler potential G-invariant up to a K"ahler transformation on the submanifold. Hence, in the case of an open orbit, the most general low-energy effective K"ahler potential can be written as the sum of those of the compact submanifolds and an arbitrary function of strictly G-invariants.