Four-dimensional M-theory and supersymmetry breaking

TL;DR

This paper develops a 11D M-theory framework where 4D N=1 physics emerges from a 5D intermediate step via Calabi-Yau truncations and Horava-Witten boundary conditions. By applying the Scherk-Schwarz mechanism along the fifth dimension, it derives a universal superpotential for the axion-dilaton $S$ and demonstrates a SUSY-breaking vacuum at $S=1$ with zero cosmological constant, along with a gravitino mass scaling as $m_{3/2} \sim R_5^{-2}/M_{Pl}^{(4)}$. The analysis connects the moduli $S$, $T$, and $U$ to the CY volume, the 5D radius, and complex structure, respectively, and shows how different symmetry truncations yield no-scale-like Kähler potentials and moduli stabilization patterns. Phenomenologically, choosing an intermediate $R_5^{-1} \sim 10^{11-12}$ GeV can reconcile unification and decompactification issues, offering a novel route to SUSY breaking in M-theory compactifications.

Abstract

We investigate compactifications of M-theory from $11\to 5\to 4$ dimensions and discuss geometrical properties of 4-d moduli fields related to the structure of 5-d theory. We study supersymmetry breaking by compactification of the fifth dimension and find that an universal superpotential is generated for the axion-dilaton superfield $S$. The resulting theory has a vacuum with $<S>=1$, zero cosmological constant and a gravitino mass depending on the fifth radius as $m_{3/2} \sim R_5^{-2}/M_{Pl}$. We discuss phenomenological aspects of this scenario, mainly the string unification and the decompactification problem.