M-Theory on Eight-Manifolds

TL;DR

This paper explores specific compactifications of M-theory on eight-manifolds, demonstrating that non-zero four-form fluxes can preserve supersymmetry with a warp factor and Kähler internal geometry.

Contribution

It shows that M-theory compactifications on eight-manifolds can preserve N=2 supersymmetry with non-zero fluxes and a conformally Kähler internal space, incorporating warp factors and Chern-Simons corrections.

Findings

Non-zero four-form fluxes can preserve supersymmetry.

Internal space can be conformally Kähler and Ricci flat.

Warp factor is essential due to Chern-Simons corrections.

Abstract

We show that in certain compactifications of ${\cal M}$-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 K\"ahler, it can be conformally transformed to a metric that is K\"ahler and Ricci flat, so that the internal manifold has $SU(4)$ holonomy.