Field equations and spontaneous compactification in quasi-Riemannian theories of gravity.

Abstract

We construct gravitational as well as fermionic action integrals for Weinberg's quasi-Riemannian theories of gravity in d dimensions. We investigate the possibilities of obtaining spontaneously compactifying solutions with G/sub T/ = SO(1,D-1) x G/sub T//sup prime/ where G/sub T//sup prime/is contained inBSO(d-D), 4< or =D< or =d. For G/sub T//sup prime/ = SO(d-D) we show that they are unlikely to have G-invariant solutions of the form (Minkowski)/sub 4/ x G/H, while we explicitly construct this type of solution for G/sub T//sup prime/ = H. We also present several fermionic Lagrangians and briefly discuss the chirality problem.