Vacuum Stability in Heterotic M-Theory

TL;DR

The paper addresses stabilizing all moduli in strongly coupled heterotic string theory (heterotic M-theory) by combining flux-induced potentials, gaugino condensation with threshold corrections, and non-perturbative membrane instantons, including vector-bundle Pfaffians and five-brane dynamics. A controlled analytic setup with a single Kahler modulus, a transition vector-bundle modulus, and a bulk five-brane demonstrates a fully stabilized AdS vacuum, with moduli values in phenomenologically viable ranges and the cosmological constant set by the flux-induced superpotential scale. The main contributions include a concrete mechanism to fix complex structure, dilaton, Kahler, bundle, and five-brane moduli in a single framework, and the demonstration that all moduli can be fixed while maintaining supersymmetry in the moduli sector and soft SUSY breaking in gravity/matter sectors via gaugino condensation. The work advances heterotic model-building by integrating fluxes, threshold effects, and brane dynamics, and discusses prospects for uplifting to a metastable de Sitter vacuum.

Abstract

The problem of the stabilization of moduli is discussed within the context of compactified strongly coupled heterotic string theory. It is shown that all geometric, vector bundle and five-brane moduli are completely fixed, within a phenomenologically acceptable range, by non-perturbative physics. This result requires, in addition to the full space of moduli, non-vanishing Neveu-Schwarz flux, gaugino condensation with threshold corrections and the explicit form of the Pfaffians in string instanton superpotentials. The stable vacuum presented here has a negative cosmological constant. The possibility of ``lifting'' this to a metastable vacuum with positive cosmological constant is briefly discussed.