Heterotic domain wall solutions and SU(3) structure manifolds

TL;DR

This paper explores heterotic string compactifications on SU(3) structure manifolds, introducing additional fluxes and explicit solutions to better understand the conditions for supersymmetric vacua.

Contribution

It extends previous analyses by including two omitted fluxes and providing explicit flux solutions as functions of torsion classes, aiding in the identification of valid heterotic vacua.

Findings

More general torsion class solutions are found.

Explicit flux solutions are derived.

The approach helps verify Bianchi identities and supersymmetry conditions.

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.