Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity

Abstract

We dimensionally reduce the ten dimensional heterotic action on spacetimes of the form ${\mathcal{M}}_{(2,1)}\times Y$, where ${\mathcal{M}}_{(2,1)}$ is three dimensional maximally symmetric Anti de Sitter or Minkowski space, and $Y$ is a compact seven dimensional manifold with $G_2$ structure. In doing so, we derive the real superpotential functional of the corresponding three dimensional $\mathcal{N}=1$ theory. We confirm that extrema of this functional precisely correspond to supersymmetric heterotic compactifications on manifolds of $G_2$ structure. We make some comments on the role of the superpotential functional with respect to the coupled moduli problem of instanton bundles over $G_2$ manifolds.

29 pages; v2 minor edits, matches published version