Leaps and bounds towards scale separation

TL;DR

This paper establishes rigorous bounds on the Kaluza-Klein scale in gravity compactifications using Bakry-Émery geometry, analyzing local behaviors in type IIA solutions and their implications for scale separation.

Contribution

It introduces a novel application of Bakry-Émery geometry to derive bounds on the KK scale and reexamines local behaviors in type IIA supersymmetric solutions.

Findings

Derived general bounds on KK scale in terms of Planck mass and internal diameter.

Found that local O6-plane behavior cannot be smoothed out, leading to a formal smeared O4.

Provided insights into the limitations of scale separation in certain gravity theories.

Abstract

In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry--\'Emery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.