Supersymmetry breaking in M-theory and quantization rules

TL;DR

The paper investigates supersymmetry breaking in M-theory via Scherk–Schwarz compactification from $11d$ to $4d$, showing that the breaking is driven by Kähler moduli while the dilaton $S$ and complex-structure moduli are stabilized by a generated superpotential. Through explicit truncations, it demonstrates no-scale structures and equal-moduli masses, with hypermultiplets not contributing to breaking and the goldstino identified with the fifth gravitino component $\Psi_5$. It also establishes Rohm–Witten–type quantization rules for the strong-coupling background fluxes and analyzes the impact of a boundary gaugino condensate, which shifts $S$ and creates a boundary-volume asymmetry while preserving a zero cosmological constant at tree level. Collectively, these results provide a coherent strong-coupling mechanism for SUSY breaking in M-theory and connect it to non-perturbative flux quantization, with the condensation scale naturally set by $M_{11}$.

Abstract

We analyze in detail supersymmetry breaking by compactification of the fifth dimension in M-theory in the compactification pattern $11d \to 5d \to 4d$ and find that a superpotential is generated for the complex fields coming from $5d$ hypermultiplets, namely the dilaton $S$ and the complex structure moduli. Using general arguments it is shown that these fields are always stabilized such that they don't contribute to supersymmetry breaking, which is completely saturated by the Kähler moduli coming from vector multiplets. It is shown that this mechanism is the strong-coupling analog of the Rohm-Witten quantization of the antisymmetric tensor field strength of string theories. The effect of a gaugino condensate on one of the boundaries is also considered.