Universal bose-fermi mass-relations in kaluza-klein supergravity and harmonic analysis on coset manifolds with killing spinors

Universal mass-relations between Bose and Fermi modes are obtained via general relations existing among the spectra of invariant operators on coset manifolds with Killing spinors. In particular zero-modes for pseudoscalars, spinors, and Lichnerowitz scalars are always related to the isometry and cohomology properties of the manifold. The structure of the four-dimensional supersymmetry rules on physical modes is given. Furthermore, the harmonics of the possible massless multiplets, namely, the gravitational multiplet, the Killing gauge multiplet, and the Betti gauge multiplet, are exhibited for general manifolds. Comments on matter and quasi-massless multiplets conclude the paper