Supersymmetry breaking in the effective Horava-Witten supergravity and quantization rules

We analyze in detail supersymmetry breaking by compactification of the fifth dimension in M-theory in the compactification pattern 11d → 5d → 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.