Hierarchies from Fluxes in String Compactifications

TL;DR

This paper shows how warped string compactifications can naturally generate large physical scale hierarchies, with specific examples in IIB and F-theory involving flux choices that determine the hierarchy.

Contribution

It demonstrates the realization of hierarchy-generating warped compactifications within string theory, linking flux choices to physical scale hierarchies in concrete models.

Findings

Hierarchies are fixed by RR and NS fluxes in compactifications.

Examples include IIB orientifold and F-theory on Calabi-Yau four-folds.

Hierarchy reflects chiral symmetry breaking scale in dual gauge theory.

Abstract

Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and F-theory compactifications on Calabi-Yau four-folds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining N=1 supersymmetric gauge theory,and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.