Supersymmetry breaking in M-theory and gaugino condensation

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 $\rho$ is at an intermediate scale ${\rho }^{-1}\sim 10^{12}$ GeV. At the lowest order, supersymmetry is broken only in the gravitational and moduli sector at a scale $m_{3/2}\sim {\rho }^{-1}$, 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 $(\sim {\rho }^{-2}/M_p)$ with matter scalars much heavier than gauginos.

Comments: 21 pages,latex + psfig.sty, 2 figures. The arguments on the equivalence have been made stronger. Other comments and 2 references are added