Holography on Tessellations of Hyperbolic Space

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice. In the 2d case we incorporate quantum gravity effects by allowing dynamical fluctuation of the tessellation