Marginal deformations of heterotic $G_2$ sigma models

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 ${\alpha }^{\prime }$ perturbation theory and study general geometries, in particular with non-vanishing torsion.

Minor changes: Added references and a section on classical symmetries. 24 pages, 1 figure, 1 table

References in corpus (5)

• Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
• Moduli Space of Torsional Manifolds
• The ${\alpha }^{\prime }$ Expansion On A Compact Manifold Of Exceptional Holonomy
• G-structures and Domain Walls in Heterotic Theories
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

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• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion