Coset spaces and ten-dimensional unified theories

Abstract

Spontaneous compactification to coset spaces is investigated in the framework of a generalised Einstein-Yang-Mills theory in ten dimensions. The pure gravity part of the field equations is taken to be most general, in the sense of containing at most second derivatives of the metric, and being compatible with energy-momentum conservation in the presence of matter fields (Lovelock conditions). It can be obtained from a sum of dimensionally continued Euler forms as a Lagrangian. Some theories are obtained which admit a maximum of four flat dimensions and, in this sense, lead naturally to a 4+6 decomposition of the ten-dimensional space. The most general left-invariant metric and differential forms are determined for all six-dimensional compact coset spaces G/H with semisimple G and rank(G)=rank(H). In particular, the two non-symmetric and non-isotropy-irreducible spaces SU(3)/U(1)*U(1) and Sp(4)/SU(2)*U(1) are treated in detail. The stability of exact solutions in the space of G-invariant field configurations is discussed.