Saltatory de Sitter String Vacua

We extend a recent scenario of Kachru, Kallosh, Linde and Trivedi to fix the string moduli fields by using a combination of fluxes and non-perturbative superpotentials, leading to de Sitter vacua. In our scenario the non-perturbative superpotential is taken to be the N=1^* superpotential for an SU(N) theory, originally computed by Dorey and recently rederived using the techniques of Dijkgraaf-Vafa. The fact that this superpotential includes the full instanton contribution gives rise to the existence of a large number of minima, increasing with N. In the absence of supersymmetry breaking these correspond to supersymmetric anti de Sitter vacua. The introduction of antibranes lifts the minima to a chain of (non-supersymmetric) de Sitter minima with the value of the cosmological constant decreasing with increasing compactification scale. Simpler cases are also discussed, including a finite instanton sum, as in the racetrack scenario. The relative semiclassical stability of these vacua is studied. Possible cosmological implications of these potentials are also discussed.