S-DUALITY AND COSMOLOGICAL CONSTANT IN STRING THEORY

The S-duality invariance of the equations of motion of four dimensiona l string effective action with cosmological constant, Lambda, is studi ed. It is demonstrated that the S-duality symmetry of the field equati ons are broken for nonzero Lambda. The ''naturalness'' hypothesis is i nvoked to argue that Lambda should remain small since exact S-duality symmetry will force the cosmological constant to vanish in the string effective action.