Moduli stabilisation in heterotic string compactifications

In this paper we analyze the structure of supersymmetric vacua incompactifications of the heterotic string on certain manifolds with SU(3)structure. We first study the effective theories obtained fromcompactifications on half-flat manifolds and show that solutions whichstabilise the moduli at acceptable values are hard to find. We then derive theeffective theories associated with compactification on generalised half-flatmanifolds. It is shown that these effective theories are consistent withfour-dimensional N=1 supergravity and that the superpotential can be obtainedby a Gukov-Vafa-Witten type formula. Within these generalised models, we findconsistent supersymmetric (AdS) vacua at weak gauge coupling, provided we allowfor general internal gauge bundles. In simple cases we perform a counting ofsuch vacua and find that a fraction of about 1/1000 leads to a gauge couplingconsistent with gauge unification.Comment: 32 pages, 3 figure