Superpotentials from flux compactifications of M-theory

In flux compactifications of M-theory a superpotential is generated whose explicit form depends on the structure group of the 7-dimensional internal manifold. In this note, we discuss superpotentials for the structure groups: G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For SU(3) structures, the non-zero flux components entering the superpotential describe an effective 1-dimensional model and a Chern-Simons model if there are SU(2) structures.Comment: 10 page

Fluxes in M-theory on 7-manifolds and G structures

We consider warp compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes and investigate the constraints imposed by supersymmetry. As long as the 7-manifold supports only one Killing spinor we infer from the Killing spinor equations that non-trivial 4-form fluxes will necessarily curve the external 4-dimensional space. On the other hand, if the 7-manifold has at least two Killing spinors, there is a non-trivial Killing vector yielding a reduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxes can be incorporated if one includes non-trivial SU(3) structures.Comment: 13 pages, Latex; minor changes & add reference

N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.Comment: 24 pages; v2: reference adde

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form \T as well as a flux 4-form \F. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We investigate the constraint \T \cdot \Psi = 0, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically

Supersymmetric AdS_5 solutions of M-theory

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.Comment: 40 pages. v2: minor changes, eqs. (2.22) and (D.12) correcte