Families of solutions of the heterotic G$_2$ system

TL;DR

This paper constructs new solutions to the heterotic G2 system on squashed 3-Sasakian manifolds, exploring the existence of AdS3 solutions and G2-instantons on these geometries.

Contribution

It introduces new families of heterotic G2 solutions on squashed homogeneous manifolds, including explicit instanton connections and analysis of solution existence.

Findings

AdS3 solutions exist for all squashing parameters except the nearly-parallel G2 case.

Constructed explicit G2-instanton connections on bundles over squashed manifolds.

Identified parameter ranges where solutions are absent, notably at the nearly-parallel G2 point.

Abstract

We construct new families of solutions of the heterotic G$_2$ system on squashed homogeneous 3-Sasakian manifolds, that is, using squashed metrics on either the 7-sphere or the Aloff-Wallach space $N_{1,1}$. We obtain AdS$_3$ solutions for all values of the squashing parameter $s$ except for the nearly-parallel G$_2$ value $s=1/\sqrt{5}$, for which we don't find any solutions. Along the process, we construct different G$_2$-instanton connections on bundles over these squashed manifolds.