Leaps and bounds towards scale separation

Understand

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.