Flux Superpotential in Heterotic M-theory

TL;DR

This paper derives the most general flux-induced superpotential for heterotic M-theory compactifications on seven-dimensional manifolds with SU(3) structure, analyzing its implications for moduli stabilization and the scalar potential.

Contribution

It provides the first comprehensive derivation of the flux superpotential in heterotic M-theory with SU(3) structure, highlighting its effects on the scalar potential and moduli stabilization.

Findings

Found a positive cosmological constant minimum at large orbifold length

Flux superpotential alone cannot stabilize the orbifold length at a de Sitter vacuum

Shows flux effects significantly influence non-perturbative stabilization mechanisms

Abstract

We derive the most general flux-induced superpotential for N=1 M-theory compactifications on seven-dimensional manifolds with SU(3) structure. Imposing the appropriate boundary conditions, this result applies for heterotic M-theory. It is crucial for the latter to consider SU(3) and not G_2 group structure on the seven-dimensional internal space. For a particular background that differs from CY(3) x S^1/Z_2 only by warp factors, we investigate the flux-generated scalar potential as a function of the orbifold length. We find a positive cosmological constant minimum, however at an undesirably large value of this length. Hence the flux superpotential alone is not enough to stabilize the orbifold length at a de Sitter vacuum. But it does modify substantially the interplay between the previously studied non-perturbative effects, possibly reducing the significance of open membrane instantons while underlining the importance of gaugino condensation.