Chiral families and stable compactifications

In the context of Einstein-Yang-Mills theories, we show that for eight-dimensional (d=8) space-times, the embedding of an SU(2)-instanton in an external gauge-group, K, leads to a stable compactification and the emergence of families of chiral families of fermions, as well as massless scalars. These latter are shown to arise for K=SO(N+4) when the SU(2)-instanton is embedded in the 3x3 upper left-corner of the (4+N)x(4xN) orthogonal matrices for K. On the other hand, for d=4+p, a spin-connection embedding in K leads to unstable compactification, whenever K is larger than the tangent-space group of the internal space Msup(p). (author)