Breaking the sanserifM-waves

Abstract

We present a systematic attempt at a classification of supersymmetric -theory solutions with zero flux; that is, 11-dimensional Lorentzian manifolds with vanishing Ricci curvature and admitting parallel spinors. We show that there are two distinct classes of solutions: static spacetimes generalizing the Kaluza-Klein monopole and non-static spacetimes generalizing the supersymmetric wave. The classification can be further refined by the holonomy group of the spacetime. The static solutions are organized according to the holonomy group of the spacelike hypersurface, whereas the non-static solutions are similarly organized by the (Lorentzian) holonomy group of the spacetime. These are subgroups of the Lorentz group which act reducibly yet indecomposably on Minkowski spacetime. We present novel constructions of non-static solutions consisting of warped products of d-dimensional pp-waves with (11-d)-dimensional manifolds admitting parallel spinors. Our construction yields local metrics with a variety of exotic Lorentzian holonomy groups.