G-Fluxes and Non-Perturbative Stabilisation of Heterotic M-Theory

TL;DR

This paper investigates how G-fluxes and non-perturbative effects from open membrane instantons stabilize moduli in heterotic M-theory compactified on a Calabi-Yau manifold with an M5 brane, leading to a positive vacuum energy and supersymmetry breaking.

Contribution

It derives the 4D supergravity potential including subleading effects, showing moduli stabilization and positive vacuum energy in heterotic M-theory with fluxes and M5 branes.

Findings

M5 brane stabilised at orbifold midpoint

Vacuum energy is positive at the minimum

Orbifold length and Calabi-Yau volume are stabilized by G-fluxes

Abstract

We examine heterotic M-theory compactified on a Calabi-Yau manifold with an additional parallel M5 brane. The dominant non-perturbative effect stems from open membrane instantons connecting the M5 with the boundaries. We derive the four-dimensional low-energy supergravity potential for this situation including subleading contributions as it turns out that the leading term vanishes after minimisation. At the minimum of the potential the M5 gets stabilised at the middle of the orbifold interval while the vacuum energy is shown to be manifestly positive. Moreover, induced by the non-trivial running of the Calabi-Yau volume along the orbifold which is driven by the G-fluxes, we find that the orbifold-length and the Calabi-Yau volume modulus are stabilised at values which are related by the G-flux of the visible boundary. Finally we determine the supersymmetry-breaking scale and the gravitino mass for this open membrane vacuum.