Stabilizing dilaton and moduli vacua in string and M--Theory cosmology

TL;DR

This work shows that non-trivial form fields in type II string theory and M--theory generate an effective potential for the dilaton and internal moduli, enabling stable vacua during cosmological evolution. By analyzing a simple toy model and a broad cosmological framework, the authors demonstrate that stabilization hinges on the interplay between solitonic and electric form-field configurations, with form-field charges fixing the vacuum values. In type II they argue that dilaton stabilization requires a combination of NS and RR solitons after modulus stabilization by nonperturbative effects, while in M--theory moduli can be stabilized purely by form-fields and curvature, sometimes preserving portions of supersymmetry. These results provide a mechanism for achieving finite, stable dilaton/moduli vacua in a cosmological context, potentially aligning high-energy string theory with low-energy physics and cosmology.

Abstract

We show how non-trivial form fields can induce an effective potential for the dilaton and metric moduli in compactifications of type II string theory and M-theory. For particular configurations, the potential can have a stable minimum. In cosmological compactifications of type II theories, we demonstrate that, if the metric moduli become fixed, this mechanism can then lead to the stabilization of the dilaton vacuum. Furthermore, we show that for certain cosmological M-theory solutions, non-trivial forms lead to the stabilization of moduli. We present a number of examples, including cosmological solutions with two solitonic forms and examples corresponding to the infinite throat of certain p-branes.