The Boundaries of KKLT

TL;DR

This paper investigates the higher-dimensional geometric origins of de Sitter space in KKLT constructions, focusing on the role of the radion and conifold instability, and how these affect stability and supersymmetry breaking in string compactifications.

Contribution

It introduces a 5d model with a Goldberger-Wise stabilization mechanism to analyze de Sitter solutions and conifold instability in KKLT, providing new insights into stability and hierarchy issues.

Findings

Radion field controls throat length and stability.

Conifold instability linked to radion potential destabilization.

Multiple throats can generate hierarchies in supersymmetry breaking.

Abstract

We consider the conundrum of generating de Sitter space from higher-dimensional geometry, with particular attention to KKLT-type constructions arXiv:hep-th/0301240 and their 5d implications. We show that even in the probe approximation with small $g_s$, a consistent higher-dimensional solution requires a deformation of a modulus field playing the role of a Goldberger-Wise stabilizing field in Randall-Sundrum type geometries that occurs through a shift in a the throat length. We identify the light radion field that sets the length of the throat, whose origin is the dynamical conifold deformation parameter. By analyzing the theory as a 5d model of mismatched branes in AdS5 space with a GW stabilization mechanism, we show how energy (and supersymmetry breaking) is transferred to both the IR and UV regions of the throat to generate a consistent 4d de Sitter sliced geometry. This should help resolve some of the recent apparent paradoxes in explicit higher-dimensional constructions. Moreover, the radion gives insight into the potential for the previously identified ``conifold instability". We argue that this instability would be a destabilization of the potential for the radion in KKLT, which can occur when the perturbation is too large. If indeed $\sqrt{g_s}M$ is too small, the radion would enter on its runaway direction and the conifold deformation would shrink to zero size. It is difficult to satisfy the required bound and a) maintain a hierarchy in the simpler CY manifolds and b) complete the cosmological phase transition into the stabilized throat, We also discuss the implications of this type of setup for supersymmetry breaking, and how multiple throats can introduce hierarchies of supersymmetry breaking masses, even in an anomaly-mediated scenario. In an appendix we consider general compactification constraints.