de Sitter Space in Non-Critical String Theory

TL;DR

This paper explores supercritical string theories in high dimensions, analyzing de Sitter vacua stability, decay mechanisms, and flux models, with implications for cosmological constant reduction and the stability of de Sitter space.

Contribution

It introduces supercritical string models with fluxes and analyzes their vacuum stability, decay processes, and implications for cosmological constant reduction.

Findings

Large potential barriers can stabilize de Sitter vacua against decay.

Decays involving bubble walls crossing the horizon are argued to be unphysical.

Flux models can prevent decay to linear dilaton regions, supporting stable de Sitter vacua.

Abstract

Supercritical string theories in D>10 dimensions with no moduli are described, generalizing the asymmetric orientifold construction of one of the authors. By taking the number of dimensions to be large and turning on fluxes, dilaton potentials are generated with nontrivial minima at arbitrarily small cosmological constant and D-dimensional string coupling, separated by a barrier from a flat-space linear dilaton region, but possibly suffering from strong coupling problems. The general issue of the decay of a de Sitter vacuum to flat space is discussed. For relatively small barriers, such decays are described by gravitational instantons. It is shown that for a sufficiently large potential barrier, the bubble wall crosses the horizon. At the same time the instanton decay time exceeds the Poincare recurrence time. It is argued that the inclusion of such instantons is neither physically meaningful nor consistent with basic principles such as causality. This raises the possibility that such de Sitter vacua are effectively stable. In the case of the supercritical flux models, decays to the linear dilaton region can be forbidden by such large barriers, but decays to lower flux vacua including AdS minima nevertheless proceed consistently with this criterion. These models provide concrete examples in which cosmological constant reduction by flux relaxation can be explored.