Gaugino condensation in M theory on $S^1{/Z}_2$

In the low energy limit of M theory on $S^1{/Z}_2$, we calculate the gaugino condensate potential in four dimensions using the background solutions due to Hořava. We show that this potential is free of delta-function singularities and has the same form as the potential in the weakly coupled heterotic string. A general flux quantization rule for the three-form field of M theory on $S^1{/Z}_2$ is given and checked in certain limiting cases. This rule is used to fix the free parameter in the potential originating from a zero mode of the form field. Finally, we calculate soft supersymmetry breaking terms. We find that corrections to the Kähler potential and the gauge kinetic function, which can be large in the strongly coupled region, contribute significantly to certain soft terms. In particular, for supersymmetry breaking in the $T$-modulus direction, the small values of gaugino masses and trilinear couplings that occur in the weakly coupled, large radius regime are enhanced to order $m_{3/2}$ in M theory. The scalar soft masses remain small even, in the strong coupling M-theory limit.