$G_2$ flux compactifications

TL;DR

This paper derives and analyzes the three-dimensional $ =1$ effective theories from compactifying all five string theories on $G_2$-structured manifolds, including fluxes, moduli, and gauge sectors.

Contribution

It provides a unified framework for $G_2$ flux compactifications across all string theories, extending previous work by including more fields and fluxes.

Findings

Explicit flux compactification models with full moduli dependence

Unified description of type IIA, IIB, I, and heterotic theories in 3D

Organized in terms of real superpotential in 3D $ =1$ supergravity

Abstract

We derive the three-dimensional $\mathcal{N}=1$ effective theories obtained by compactifying all five ten-dimensional string theories on generic seven-dimensional manifolds with $G_2$ structure. The resulting flux compactifications are worked out explicitly, including the full moduli dependence of the scalar potential, kinetic terms, axionic sectors, gauge fields, St\"uckelberg couplings, and the allowed geometric and form-flux data. Our results extend previous analyses by incorporating fields and fluxes that are generically present in $G_2$ reductions, and provide a unified framework for comparing type IIA, type IIB, type I and heterotic compactifications to three dimensions. In particular, the effective theories organize naturally in terms of the real superpotential formulation of three-dimensional $\mathcal{N}=1$ supergravity, making the relation between fluxes, torsion, Chern--Simons data, and moduli potentials manifest.