Harmonic expansions for (4+K)-dimensional Rarita-Schwinger fields on coset spaces and effective Lagrangian in four dimensions

Harmonic expansions on the internal compact coset manifold G/H for the (4+K)-dimensional Rarita-Schwinger fields are developed. The dimensional reduction of the Rarita-Schwinger Lagrangian coupled to gravity in 4+K dimensions is carried out using these expansions. The resulting four-dimensional effective Lagrangian describes an infinite tower of massive spin-(3/2) and spin-1/2 fields, coupled minimally and nonminimally to gauge fields. The masses of the Dirac fields are not given by the eigenvalues of the internal Rarita-Schwinger operator as is usually supposed.