Marginal deformations of heterotic $G_2$ sigma models

TL;DR

This paper links the marginal deformations of heterotic G2 sigma models to cohomology classes of a worldsheet BRST operator, establishing a connection with supergravity moduli space and analyzing geometries with torsion.

Contribution

It identifies the marginal deformations of heterotic G2 sigma models with BRST cohomology classes and relates them to supergravity moduli, including non-vanishing torsion geometries.

Findings

Marginal deformations correspond to BRST cohomology classes.

Cohomologies are isomorphic to supergravity moduli space.

Analysis includes geometries with non-zero torsion.

Abstract

Recently, the infinitesimal moduli space of heterotic $G_2$ compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST operator. This BRST operator is nilpotent if and only if the target space geometry satisfies the heterotic supersymmetry conditions. We relate this to the supergravity approach by showing that the corresponding cohomologies are indeed isomorphic. We work at tree-level in $\alpha'$ perturbation theory and study general geometries, in particular with non-vanishing torsion.