Heterotic domain wall solutions and SU(3) structure manifolds

Abstract

We examine compactifications of heterotic string theory on manifolds with SU(3) structure. In particular, we study N = 1/2 domain wall solutions which correspond to the perturbative vacua of the 4D, N =1 supersymmetric theories associated to these compactifications. We extend work which has appeared previously in the literature in two important regards. Firstly, we include two additional fluxes which have been, heretofore, omitted in the general analysis of this situation. This allows for solutions with more general torsion classes than have previously been found. Secondly, we provide explicit solutions for the fluxes as a function of the torsion classes. These solutions are particularly useful in deciding whether equations such as the Bianchi identities can be solved, in addition to the Killing spinor equations themselves. Our work can be used to straightforwardly decide whether any given SU(3) structure on a six-dimensional manifold is associated with a solution to heterotic string theory. To illustrate how to use these results, we discuss a number of examples taken from the literature.

34 pages, minor corrections in second version

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• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
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• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
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• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds
• $Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity