Stabilizing Moduli with a Positive Cosmological Constant in Heterotic M-Theory
Volker Braun, Burt A. Ovrut
TL;DR
The paper investigates moduli stabilization in strongly coupled heterotic M-theory with bulk branes, demonstrating that a pure five-brane setup fixes all moduli but yields a large negative cosmological constant. By introducing anti-five-branes, the authors add a controlled uplift term that can raise the vacuum energy to a small positive, metastable de Sitter minimum while preserving moduli stabilization and breaking $N=1$ supersymmetry. The analysis is carried out in simplified yet representative sectors (starting with $h^{1,1}=1$ and extending to $h^{1,1}=2$), and is then specialized to the Minimal Heterotic Standard Model, where anomaly cancellation fixes brane content and explicit Kahler moduli regions are identified where the observable bundle remains slope-stable. The results show that all moduli can be stabilized in a metastable de Sitter vacuum with a phenomenologically viable positive cosmological constant and a realistic MSSM-like visible sector, providing a concrete string-theoretic mechanism for SUSY breaking and cosmological constant tuning.
Abstract
It is shown that strongly coupled heterotic M-theory with anti-five-branes in the S^1/Z_2 bulk space can have meta-stable vacua which break N=1 supersymmetry and have a small, positive cosmological constant. This is demonstrated for the "minimal" heterotic standard model. This vacuum has the exact MSSM matter spectrum in the observable sector, a trivial hidden sector vector bundle and both five-branes and anti-five-branes in the bulk space. The Kahler moduli for which the cosmological constant has phenomenologically acceptable values are shown to also render the observable sector vector bundle slope-stable. A corollary of this result is that strongly coupled M-theory vacua with only five-branes in the S^1/Z_2 interval may have stabilized moduli, but at a supersymmetry preserving minimum with a large, negative cosmological constant.