$Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity

TL;DR

This paper explores heterotic string compactifications on $Spin(7)$ manifolds with multiple external directions, revealing new solutions with more general superpotentials and potential phenomenological relevance.

Contribution

It introduces a class of $Spin(7)$ compactifications with multiple external directions that extend previous solutions and exhibit superpotentials similar to non-geometric flux compactifications.

Findings

Found new $Spin(7)$ solutions allowing more general internal geometries.

Identified superpotentials resembling those in non-geometric flux compactifications.

Demonstrated potential for lifting to maximally symmetric vacua via non-perturbative effects.

Abstract

We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a $Spin(7)$ manifold, which leads to a $1/4$-BPS four-dimensional supersymmetric perturbative vacuum breaking all but one supercharge. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to maximal symmetry by some non-perturbative or higher-order effect.