Prof Andre Lukas

Abstract:

Compactifications of the heterotic string with NS flux normally require non Calabi-Yau internal spaces which are complex but no longer Kähler. We point out that this conclusion rests on the assumption of a maximally symmetric four-dimensional space-time and can be avoided if this assumption is relaxed. Specifically, it is shown that an internal Calabi-Yau manifold is consistent with the presence of NS flux provided four-dimensional space-time is taken to be a domain wall. These Calabi-Yau domain wall solutions can still be associated with a covariant four-dimensional N = 1 supergravity. In this four-dimensional context, the domain wall arises as the "simplest" solution to the effective supergravity due to the presence of a flux potential with a runaway direction. Our main message is that NS flux is a legitimate ingredient for moduli stabilisation in heterotic Calabi-Yau models. Ultimately, the success of such models depends on the ability to stabilise the runaway direction and thereby "lift" the domain wall to a maximally supersymmetric vacuum. © 2013 SISSA, Trieste, Italy.

Abstract:

We study heterotic string compactifications on nearly Kähler homogeneous spaces, including the gauge field effects which arise at order α′. 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 α′ 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 Kähler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level. © 2013 SISSA, Trieste, Italy.

Abstract:

We discuss the use of gauge fields to stabilize complex structure moduli in Calabi-Yau three-fold compactifications of heterotic string and M-theory. The requirement that the gauge fields in such models preserve supersymmetry leads to a complicated landscape of vacua in complex structure moduli space. We develop methods to systematically map out this multi-branched vacuum space, in a computable and explicit manner. In analysing the resulting vacua, it is found that the associated Calabi-Yau three-folds are sometimes stabilized at a value of complex structure resulting in a singular compactification manifold. We describe how it is possible to resolve these singularities, in some cases, while maintaining computational control over the moduli stabilization mechanism. The discussion is illustrated throughout the paper with explicit worked examples. © 2013 SISSA, Trieste, Italy.