Moduli stabilisation in early superstring cosmology

Abstract

We study the cosmological evolution induced by the free energy of a string gas at finite temperature. We first consider the maximally supersymmetric heterotic string in the weak coupling regime in dimension D ≥ 4. The free energy develops local minima associated to some gauge symmetry enhancement induced by perturbative states. This can stabilize all heterotic moduli except the dilaton. By string-string S-dualities, it follows that the dual type I moduli can be stabilized by either non perturbative D-string states or perturbative open string states. We next consider the type II string compactified on Calabi-Yau three-folds, which has \U0001d4a9 = 2 supersymmetry in D = 4. The moduli space has singular loci where the Calabi-Yau space undergoes extremal transitions, accompanied with either conifold transitions or certain gauge symmetry enhancement. Also the free energy reaches local minima due to the emergence of extra non perturbative massless modes. Consequently, the type II moduli are attracted to these singular loci. Using the type II/heterotic string duality, we can stabilize the dual heterotic moduli, and in particular it is possible to stabilize the heterotic dilaton.