  We consider a recent proposal to solve the cosmological constant problem
within the context of brane world scenarios with infinite volume extra
dimensions. In such theories bulk can be supersymmetric even if brane
supersymmetry is completely broken. The bulk cosmological constant can
therefore naturally be zero. Since the volume of the extra dimensions is
infinite, it might appear that at large distances one would measure the bulk
cosmological constant which vanishes. We point out a caveat in this argument.
In particular, we use a concrete model, which is a generalization of the
Dvali-Gabadadze-Porrati model, to argue that in the presence of non-zero brane
cosmological constant at large distances such a theory might become effectively
four dimensional. This is due to a mass gap in the spectrum of bulk graviton
modes. In fact, the corresponding distance scale is set precisely by the brane
cosmological constant. This phenomenon appears to be responsible for the fact
that bulk supersymmetry does not actually protect the brane cosmological
constant.
