The heterotic $G_2$ moduli space metric

Abstract

In this article we dimensionally reduce a heterotic supergravity on a $G_2$ background with Minkowski spacetime using a certain cohomology as a basis for the Kaluza-Klein expansion, up to and including first order in $\alpha'$. We construct the moduli space heterotic $G_2$ compactifications. The $\alpha'$-correction induces a curvature correction to the Weyl-Peterson metric. In the limit in which the $G_2$ manifold reduces to $SU(3)$, we recover known results.