Bulk supersymmetry and brane cosmological constant

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. We propose a setup where unbroken bulk supersymmetry appears to protect the brane cosmological constant. This is due to a non-trivial scalar potential in the bulk which implies a non-trivial profile for a bulk scalar field. In the presence of the latter bulk supersymmetry appears to be incompatible with non-vanishing brane cosmological constant. Moreover, in this setup the corresponding domain wall interpolates between an AdS and the Minkowski vacua, so that the weak energy condition is not violated.