[Paper Review] de Sitter Space in Non-Critical String Theory

Alexander Maloney, Eva Silverstein+1 more|ArXiv.org|May 30, 2002

Black Holes and Theoretical PhysicsPhysics and Astronomy30 references92 citations

TL;DR

This paper constructs de Sitter (dS) vacua in non-critical string theory using a generalized asymmetric orientifold in high spacetime dimensions (D > 10), where fluxes generate a dilaton potential with a nontrivial minimum at a parametrically small cosmological constant and weak string coupling. The key result is that large potential barriers suppress decay to flat space via gravitational instantons, suggesting effective stability of dS vacua—though decays to lower flux vacua, including AdS, remain consistent with causality and unitarity.

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.

Motivation & Objective

• To construct de Sitter vacua in non-critical string theory without moduli, addressing the lack of stable dS solutions in string theory.
• To explore whether dS vacua can be effectively stable by suppressing decay to flat space via large potential barriers.
• To analyze the consistency of gravitational instanton processes in dS quantum gravity, particularly when instantons become superhorizon-sized.
• To investigate whether flux relaxation in high-dimensional supercritical string theory can realize cosmological constant reduction with parametrically small values.
• To assess the validity of semiclassical instanton decay processes in dS space, especially in relation to causality and the Poincaré recurrence time.

Proposed method

• Generalizes the asymmetric orientifold construction to D > 10 dimensions, introducing a new parameter D to control the number of degrees of freedom.
• Uses RR fluxes and the Bousso-Polchinski mechanism to generate a dilaton potential with a nontrivial minimum at small cosmological constant.
• Scales the number of RR fields as n_RR = 2^D, enabling parametric control over the cosmological constant and string coupling.
• Analyzes decay processes via gravitational instantons, focusing on the transition from dS to flat space through domain walls.
• Applies a criterion based on horizon-crossing and causality to assess the physical consistency of instanton processes.
• Evaluates D-brane-induced decays between flux vacua, computing tensions and comparing them to critical tensions to determine decay feasibility.

Experimental results

Research questions

• RQ1 Can de Sitter vacua be constructed in non-critical string theory without moduli, using fluxes and high-dimensional compactifications?
• RQ2 Under what conditions does the decay of a dS vacuum to flat space become physically inconsistent due to horizon-crossing instantons?
• RQ3 Does the Poincaré recurrence time provide a bound on the validity of semiclassical instanton decay in dS space?
• RQ4 Can flux relaxation in high-D supercritical string theory lead to cosmological constant reduction with parametrically small values?
• RQ5 Are decays to AdS or lower dS vacua consistent with causality and unitarity when the instanton size exceeds the horizon?

Key findings

• The cosmological constant at the dS minimum is parametrically small, scaling as 2^{-D} for the lowest-lying vacua.
• The string coupling at the dS minimum is parametrically weak, scaling as 1/b where b ~ 2^{D/4}.
• The potential barrier to the linear dilaton region becomes parametrically large with increasing D, suppressing decay via gravitational instantons.
• For sufficiently large barriers, the instanton decay process becomes superhorizon-sized, violating causality and unitarity, and the decay time exceeds the Poincaré recurrence time.
• Decays to lower flux vacua, including AdS, remain consistent with the causality criterion, as their D-brane tensions are below the critical threshold.
• The degeneracy of vacua favors transitions to less negative cosmological constants, suppressing deep AdS decay endpoints despite their availability.