I actually want to know whether space-time supersymmetry is important for string theory consistency? I see that NS and GS supersymmetric strings have worldsheet supersymmetry, but the first one does not have a manifest space-time SUSY while the second one has it manifest. I want to know if this space-time SUSY is really having an impact on string theory.
I know the answer is Yes, but in which way it effects the consistency of string theory? (compactification?)
Edit- I would like to add that the only way I think this space-time SUSY adds to string theory is the notion of a constant covariant spinor, which gives the Calabi-Yau manifold for compactification. Is this the necessity of space-time SUSY? And what else can we say about it in connection to string theory.