M-Theory on Seven Manifolds with G-fluxes

We compactify M-theory on seven-manifolds with a warp-factor and G-fluxes on the internal space. Because of non-zero G-fluxes, we are forced to adopt a Majorana supersymmetry spinor ansatz which does not have the usual direct product structure of two lower dimensional Majorana spinors. For the spinor ansatz that we choose, we find that supersymmetry puts strong constraints on the internal space namely that it must be conformal to a Ricci-flat seven-manifold of the form $X^7= X^6 \times X^1$. The holonomy of $X^6$ must be larger than 1 if the warp-factor is to be non-trivial. The warp-factor depends only on the $X^1$ direction and is singular. We argue that to avoid this singularity one has to embed this solution in a Horava-Witten setup and thus has natural links to much studied brane-world scenarios.