Implementing holographic projections in Ponzano--Regge gravity

TL;DR

This paper explores holographic projections within Ponzano-Regge quantum gravity, analyzing how bulk and boundary theories behave differently in the semi-classical and quantum regimes, respectively.

Contribution

It introduces a method to implement holographic projections in Ponzano-Regge gravity, linking bulk path-sums to boundary quantum states.

Findings

Bulk partition function approaches semi-classical limit.

Boundary state functional remains fully quantum.

Discussion of boundary theory properties.

Abstract

We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a semi-classical limit while the boundary state functional remains quantum-mechanical. The properties of the resulting boundary theory are discussed.