The heterotic G${}_2$ system with reducible characteristic holonomy

Abstract

We construct solutions to the heterotic G${}_2$ system on almost contact metric manifolds with reduced characteristic holonomy. We focus on $3$-$(\hat{I}\pm ,\hat{I}´)$-Sasaki manifolds and $(\hat{I}\pm ,\hat{I}´)$-Sasaki manifolds, the latter being a convenient reformulation of spin $\hat{I}\cdot$-Einstein $\hat{I}\pm$-Sasaki manifolds. Investigating a $1$-parameter family of G${}_2$-connections on the tangent bundle, we obtain several approximate solutions as well as one new class of exact solutions on degenerate $3$-$(\hat{I}\pm ,\hat{I}´)$-Sasaki manifolds.

48 pages; v2: typos fixed, matches published version