Moduli Stabilising in Heterotic Nearly Kähler Compactifications

Abstract: We study heterotic string compactifications on nearly K\"ahler homogeneous spaces, including the gauge field effects which arise at order \alpha'. Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry conditions to this order. The four-dimensional external space-time consists of a domain wall solution with moduli fields varying along the transverse direction. We find that the inclusion of \alpha' corrections improves the moduli stabilization features of this solution. In this case, one of the dilaton and the volume modulus asymptotes to a constant value away from the domain wall. It is further shown that the inclusion of non-perturbative effects can stabilize the remaining modulus and "lift" the domain wall to an AdS vacuum. The coset SU(3)/U(1)^2 is used as an explicit example to demonstrate the validity of this AdS vacuum. Our results show that heterotic nearly K\"ahler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level.