Compactification of D = 11 supergravity on spaces of exceptional holonomy

We investigate the compactification of D = 11 supergravity to D = 5,4,3, on compact manifolds of holonomy SU(3) (Calabi-Yau), G2, and Spin(7), respectively, making use of examples of the latter two cases found recently by Joyce. In each case the lower dimensional theory is a Maxwell/Einstein supergravity theory. We find evidence for an equivalence, in certain cases, with heterotic string compactifications from D = 10 to D = 5,4,3, on compact manifolds of holonomy SU(2) (K3 × S1), SU(3), and G2, respectively. Calabi-Yau manifolds with Hodge numbers h1,1 = h1,2 = 19 play a significant role in the proposed equivalences.