CP violation and gravity as the weakest force

We argue that CP violation has rather dramatic impact on the "gravity as the weakest force" conjecture. Namely we find that new ultraviolet scale must be $\Lambda \lesssim \theta g^3 M_P$, where $\theta$ is an effective parameter describing CP violation and $g$ is the gauge coupling constant. The bound implies that CP-conserving limit is discontinuous, and possibly indicates that the class of effective theories with strict CP conservation is inconsistent with a fundamental theory incorporating quantum gravity. At the same time, the mass hierarchy problem can be explained due to the smallness of the CP violation, $\theta \sim 10^{-15}$ or so.Comment: 4 page

Diffeomorphism-invariant noncommutative gravity with twisted local Lorentz invariance

We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler compared to the existing formulations of noncommutative gravity.Comment: 7 pages; v2 to be published in EJT