Heterotic Moduli Stabilisation and Non-Supersymmetric Vacua

TL;DR

This paper investigates moduli stabilization in heterotic string compactifications, demonstrating the existence of perturbative, non-supersymmetric AdS vacua with stabilized moduli, even when considering non-perturbative effects.

Contribution

It provides the first analytic construction of perturbative, non-supersymmetric AdS vacua in heterotic string theories with stabilized moduli.

Findings

Perturbative vacua break supersymmetry and stabilize all T-moduli and the dilaton.

Stable AdS vacua exist under specific conditions on D-terms.

Non-perturbative effects do not destabilize these vacua.

Abstract

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, $\partial_iV_F=\partial_iV_D=0$, 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.