Heterotic Calabi-Yau Compactifications with Flux

TL;DR

This paper demonstrates that heterotic string compactifications with NS flux can preserve Calabi-Yau geometry if the four-dimensional space-time is a domain wall, opening new avenues for moduli stabilization.

Contribution

It shows that Calabi-Yau manifolds can support NS flux when the four-dimensional space-time is a domain wall, challenging previous assumptions and enabling flux-based moduli stabilization.

Findings

Calabi-Yau with NS flux is consistent with domain wall space-time.

Domain walls arise as solutions in effective supergravity with flux potential.

Flux can stabilize moduli by lifting the runaway direction.

Abstract

Compactifications of the heterotic string with NS flux normally require non Calabi-Yau internal spaces which are complex but no longer K\"ahler. 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 stabilization in heterotic Calabi-Yau models. Ultimately, the success of such models depends on the ability to stabilize the runaway direction and thereby "lift" the domain wall to a maximally supersymmetric vacuum.