Supersymmetric models for quarks and leptons with nonlinearly realizedE8symmetry

We propose three supersymmetric nonlinear sigma models with global symmetry E/sub 8/. The models can accommodate three left-handed families of quarks and leptons without incurring the Adler-Bell-Jackiw anomaly with respect to either the standard SU(3) x SU(2) x U(1) gauge group, or the SU(5), or SO(10) grand unifying gauge group. They also predict unambiguously a right-handed, fourth family of quarks and leptons. In order to explore the structure of the models, we develop a differential-form formulation of the Kahler manifolds, resulting in general expressions for the curvature tensors and other geometrical objects in terms of the structure constants of the algebra, and the squashing parameters. These results, in turn, facilitate a general method for determining the Lagrangian to quartic order, and so the structure of the inherent four-fermion interactions of the models. We observe that the Kahlerian condition d..omega.. = 0 on the fundamental two-form ..omega.. greatly reduces the number of the independent squashing parameters. We also point out two plausible mechanisms for symmetry breaking, involving gravity.