The heterotic $G_2$ moduli space metric

TL;DR

This paper derives the moduli space metric for heterotic G2 compactifications, including first-order alpha' corrections, and connects to known SU(3) results in a special limit.

Contribution

It constructs the heterotic G2 moduli space metric with alpha' corrections, extending previous results to include curvature effects and a specific cohomology basis.

Findings

Alpha' correction induces curvature correction to the metric

Reproduces known SU(3) results in a special limit

Provides a detailed construction of the moduli space

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.