Supersymmetric Non-Linear Lagrangians of Kahlerian Coset Spaces G/H: G=E6, E7 and E8

A simple and general procedure is given for constructing supersymmentric nonlinear σ model Lagrangian explicitly for any Kählerian coset space G/H. In particular, we derive explicit and full expressions of supersymmetric Lagrangians for the phenomenologically important manifolds G/H=E7/SU(5)×SU(3)×SU(1) and E8 /SO(10)×SU(3)×U(1), which are known to contain three generations of quarks and leptons as Nambu-Goldstone (NG) superfields. We discuss also (1) the arbitrariness of the choice of NG superfields when H contains more than one dimensional center, (2) how to gauge any subgroup of G and how to couple the system to supergravity, (3) a new anomaly of the supersymmetric nonlinear σ models induced by supergravity, etc.