Discretized gravity on the hyperbolic disk

TL;DR

This paper explores a six-dimensional lattice gravity model with extra dimensions compactified on a warped hyperbolic disk, revealing weaker coupling near the boundary and potential for high strong coupling scales.

Contribution

It introduces a discretized model of six-dimensional hyperbolic space for gravity, analyzing its coupling properties and differences from lower-dimensional or flat models.

Findings

Weaker coupling near the boundary of the hyperbolic disk.

Strong coupling scale can reach the local Planck scale near IR branes.

Lattice gravity behaves differently in hyperbolic space compared to flat or warped 5D models.

Abstract

We consider a description of lattice gravity in six dimensions, where the two extra dimensions have been compactified on a warped hyperbolic disk of constant curvature. We analyze a fine-grained latticization of the hyperbolic disk in the context of an effective theory for massive gravitons. We find that in six-dimensional warped hyperbolic space, lattice gravity appears near the boundary of the disk more weakly coupled than in discretized five-dimensional flat or warped space. Specifically, near the IR branes, the local strong coupling scale can become as large as the local Planck scale.