Weakly coupled discretized gravity

TL;DR

This paper explores discretized gravity in a 4+2 dimensional negatively curved space, showing that boundary observers can experience a strong coupling scale larger than the local Planck scale, enabling a weakly coupled boundary theory.

Contribution

It demonstrates that discretized gravity on a negatively curved disk can maintain weak coupling at scales above the local Planck scale for boundary matter.

Findings

Strong coupling scale exceeds local Planck scale for boundary observers.

Negative curvature prevents dangerous ultra-light scalar modes.

Boundary discretized gravity matches continuum theory up to the 5D Planck scale.

Abstract

We consider discretized gravity in 4+2 dimensions compactified on a disk of constant negative curvature. The curvature of the disk avoids the presence of dangerous ultra-light scalar modes but comes also along with a high multiplicity of states potentially jeopardizing a good strong-coupling behavior of the discretized theory. We demonstrate that for Standard Model matter propagating on the five-dimensional boundary submanifold of the disk, the strong coupling scale, as seen by an observer, can be parametrically larger than the local Planck scale. As a consequence, we obtain a description of weakly coupled discretized gravity on the boundary that can be compared with the continuum theory all the way up to the effective five-dimensional Planck scale.