Phenomenological Kaehler sigma models. Pt. 1

The mathematical formalism of supersymmetric sigma models is developed to the point where they can describe realistic composite models of quarks and leptons. The sigma models of interest are the effective lagrangians of confining supersymmetric gauge theories. The dynamics of the massless bound states in the gauge theory is reflected in the geometry of the target manifold of the sigma model, which is required to be a non-compact, non-homogeneous Kaehler manifold. More precisely, it is the deformation of a complex coset space anti G/K tilde such that the isometry group is just G. Special topics discussed include the construction of the most general Kaehler potential, weak gauging of isometries, four-Fermi interactions and the target manifold curvature, and soft chiral and supersymmetry breaking. (orig.)