Non-singular deformations of singular compactifications, the cosmological constant and the hierarchy problem

We consider deformations of the singular 'global cosmic string' compactific ations, known to naturally generate exponentially large scales. The deforma tions are obtained by allowing a constant-curvature metric on the brane and correspond to a choice of integration constant. We show that there exists a unique value of the integration constant that gives rise to a non-singula r solution. The metric on the brane is dS(4) with an exponentially small va lue of the expansion parameter. We derive an upper bound on the brane cosmo logical constant. We find and investigate more general singular solutions-' dilatonic global string' compactifications-and show that they can have non- singular deformations. We give an embedding of these solutions in type IIB supergravity. There is only one class of supersymmetry-preserving singular dilatonic solutions. We show that they do nor have non-singular deformation s of the type considered here.