M-theory on eight-manifolds

We show that in certain compactifications of M-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an N = 2 supersymmetry is preserved. For these compactifications a warp factor for the metric has to be taken into account, This warp factor is non-trivial in three space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi identity. While the original metric on the internal space is not Kahler, it can be conformally transformed to a metric that is Kahler and Ricci flat, so that the internal manifold has SU(4) holonomy.