JOURNAL OF HIGH ENERGY PHYSICS, v.2016, no.3, pp.177 -
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 supersym- metry, 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. (c) The Authors.