Supersymmetry breaking in M-theory and gaugino condensation

TL;DR

This paper shows that supersymmetry breaking via gaugino condensation in the strongly coupled heterotic string can be described by a Scherk–Schwarz–like coordinate-dependent compactification along the eleventh dimension in M-theory. By identifying the M-theory scale with the grand-unification mass and placing the eleventh dimension at an intermediate scale, it derives an intermediate gravitino mass $m_{3/2}\sim\rho^{-1}$ and gravity-mediated soft terms $m_{susy}\sim\rho^{-2}/M_p$, predicting a spectrum with heavy scalar masses and comparatively lighter gauginos. The authors detail the 5D bulk/4D boundary structure, compute the one-loop gravitational contributions to scalar and gaugino masses, and discuss phenomenological implications, including possible flavor problems and the need for extra matter to realize viable gaugino masses. They contrast this mechanism with alternative large-radius scenarios and outline future directions for refining the low-energy EFT and exploring other symmetry realizations.

Abstract

We argue that supersymmetry breaking by gaugino condensation in the strongly coupled heterotic string can be described by an analogue of Scherk-Schwarz compactification on the eleventh dimension in M-theory. The M-theory scale is identified with the gauge coupling unification mass, whereas the radius of the eleventh dimension $ρ$ is at an intermediate scale $ρ^{-1}\sim 10^{12}$ GeV. At the lowest order, supersymmetry is broken only in the gravitational and moduli sector at a scale $m_{3/2}\simρ^{-1}$, while it is mediated by gravitational interactions to the observable world. Computation of the mass splittings yields in general a hierarchy of soft masses at the TeV scale $(\simρ^{-2}/M_p)$ with matter scalars much heavier than gauginos.

Figures (2)

• Figure 1: One-loop (gravitational) diagrams contributing to scalar masses.
• Figure 2: One-loop (gravitational) diagrams contributing to gaugino masses.