Holography on tessellations of hyperbolic space

TL;DR

This paper investigates how boundary correlation functions for scalar fields behave on tessellated hyperbolic spaces, providing evidence that continuum relations persist despite lattice truncation.

Contribution

It demonstrates that the continuum relation between bulk mass and boundary scaling dimension remains valid on discretized hyperbolic tessellations.

Findings

Boundary correlation functions computed on tessellations match continuum predictions.

The bulk mass and boundary scaling dimension relation survives lattice truncation.

Evidence supports the robustness of holographic relations in discretized hyperbolic geometries.

Abstract

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.