Effective action of (massive) type IIA supergravity on manifolds withSU(3)structure

In this paper we consider compactifications of massive type IIA supergravity on manifolds with $SU(3)$ structure. We derive the gravitino mass matrix of the effective four-dimensional $\mathcal{N}=2$ theory and show that vacuum expectation values of the scalar fields naturally induce spontaneous partial supersymmetry breaking. We go on to derive the superpotential and the Kähler potential for the resulting $\mathcal{N}=1$ theories. As an example we consider the $SU(3)$ structure manifold $SU(3)/U(1)\times U(1)$ and explicitly find $\mathcal{N}=1$ supersymmetric minima where all the moduli are stabilized at nontrivial values without the use of nonperturbative effects.