Heterotic moduli stabilisation and non-supersymmetric vacua

We study moduli stabilisation in four-dimensional N = 1 supergravity theories which originate from compactifications of the heterotic string on certain manifolds with SU(3) structure. These theories have a non-trivial superpotential generated from geometric flux and, in general, D-terms associated to anomalous U(1) symmetries. We show that, at the perturbative level, there are no supersymmetry preserving vacua. However, subject to a certain technical condition on the D-terms which aligns the extrema of the F-term and D-term potentials, partial derivative V-i(F) = partial derivative V-i(D) = 0, we find at the perturbative level analytic stable AdS vacua which break supersymmetry. As a result, all T-moduli and the dilaton are stabilised perturbatively with supersymmetry broken at a high scale. We also show numerically that similar vacua can be found when the technical condition on the D-term is relaxed. These vacua persist in the presence of non-perturbative effects. In all cases, the vacua remain AdS.