Gaugino Condensation, Moduli Potentials and Supersymmetry Breaking in M-Theory Models

TL;DR

The paper analyzes gaugino condensation in the strongly coupled M-theory framework on $M_4 \times X \times S^1 / Z_2$, deriving the moduli-dependent 4D effective potential $V_{eff}(\sigma,\gamma)$ with a gaugino-scale $\mu(\sigma,\gamma)$ and boundary-geometry coefficients. It attempts to map this potential to a 4D $N=1$ supergravity description with a moduli-dependent superpotential $W(S,T)$, finding that the presence of both $S$ and $T$ in the gauge coupling destroys a simple perfect-square structure and raises holomorphy-consistency issues between $W$ and the gauge kinetic function $f_{ab}$. The work highlights significant conceptual and technical challenges in deriving a consistent 4D effective theory for SUSY breaking and moduli stabilization from M-theory, emphasizing the nuanced role of boundary terms $G_{11ABC}$ and the distinction between Wil{sonian and physical couplings. It suggests that, while moduli stabilization might be achievable in scenarios with boundary sources, a more careful treatment of massive-mode integration and holomorphic structure is required for a reliable low-energy description.

Abstract

We derive the explicit form, and discuss some properties of the moduli dependent effective potential arising from M-theory compactified on $M_4 \times X\times S^1 / Z_2 $, when one of the boundaries supports a strongly interacting gauge sector and induces gaugino condensation. We discuss the relation between the explicit gaugino condensate and effective superpotential formulations and find interesting differences with respect to the situation known from the weakly coupled heterotic string case. The moduli dependence of the effective potential turns out to be more complicated than expected, and perhaps offers new clues to the stabilization problem.