# Quasi-local holographic dualities in non-perturbative 3d quantum gravity

## TL;DR

This paper explores holographic dualities in three-dimensional quantum gravity using the Ponzano-Regge model, establishing connections between 3d quantum gravity and 2d statistical models within finite regions.

## Contribution

It introduces a detailed framework for holographic dualities in 3d quantum gravity with finite boundaries, utilizing the Ponzano-Regge state-sum model for explicit boundary state definitions.

## Key findings

- Explicit boundary state definitions in 3d quantum gravity.
- Holographic dualities between 3d gravity and 2d statistical models.
- Analysis of the coherent twisted torus boundary case.

## Abstract

We present a line of research aimed at investigating holographic dualities in the context of three dimensional quantum gravity within finite bounded regions. The bulk quantum geometrodynamics is provided by the Ponzano-Regge state-sum model, which defines 3d quantum gravity as a discrete topological quantum field theory (TQFT). This formulation provides an explicit and detailed definition of the quantum boundary states, which allows a rich correspondence between quantum boundary conditions and boundary theories, thereby leading to holographic dualities between 3d quantum gravity and 2d statistical models as used in condensed matter. After presenting the general framework, we focus on the concrete example of the coherent twisted torus boundary, which allows for a direct comparison with other approaches to 3d/2d holography at asymptotic infinity. We conclude with the most interesting questions to pursue in this framework.