Massless D-strings and moduli stabilization in type I cosmology

TL;DR

This paper demonstrates that in type I string cosmology, light D-string modes and duality symmetries can stabilize all internal moduli, with specific results for the volume modulus and dilaton in various dimensions.

Contribution

It shows that heterotic/type I S-duality at finite temperature can be used to achieve full moduli stabilization in type I cosmology, highlighting the role of D-string modes.

Findings

All internal moduli can be stabilized at enhanced gauge symmetry points.

The internal volume modulus remains flat in D=6, but the dilaton is stabilized.

Light D-string modes significantly influence the free energy and stabilization.

Abstract

We consider the cosmological evolution induced by the free energy F of a gas of maximally supersymmetric heterotic strings at finite temperature and weak coupling in dimension D>=4. We show that F, which plays the role of an effective potential, has minima associated to enhanced gauge symmetries, where all internal moduli can be attracted and dynamically stabilized. Using the fact that the heterotic/type I S-duality remains valid at finite temperature and can be applied at each instant of a quasi-static evolution, we find in the dual type I cosmology that all internal NS-NS and RR moduli in the closed string sector and the Wilson lines in the open string sector can be stabilized. For the special case of D=6, the internal volume modulus remains a flat direction, while the dilaton is stabilized. An essential role is played by light D-string modes wrapping the internal manifold and whose contribution to the free energy cannot be omitted, even when the type I string is at weak coupling. As a result, the order of magnitude of the internal radii expectation values on the type I side is (lambda_I alpha')^{1/2}, where lambda_I is the ten-dimensional string coupling. The non-perturbative corrections to the type I free energy can alternatively be described as effects of "thermal E1-instantons", whose worldsheets wrap the compact Euclidean time cycle.