S-duality and cosmological constant in string theory

The S-duality invariance of the equations of motion of four dimensional string effective action with cosmological constant, Λ, is studied. It is demonstrated that the S-duality symmetry of the field equations are broken for nonzero Λ. The “naturalness” hypothesis is invoked to argue that Λ should remain small since exact S-duality symmetry will force the cosmological constant to vanish in the string effective action.