Discretized gravity on the hyperbolic disk

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.