Non-Perturbative 3D Quantum Gravity: Quantum Boundary States and Exact Partition Function

TL;DR

This paper advances the understanding of 3D quantum gravity and holography by analytically computing boundary state amplitudes in the Ponzano-Regge model, revealing potential symmetries and integrability.

Contribution

It provides the first exact analytical calculation of Ponzano-Regge amplitudes with extended boundary states, connecting boundary quantum states to bulk partition functions in 3D quantum gravity.

Findings

Exact boundary amplitude calculations for extended 2D boundary states.

Regularized finite truncation of BMS character formula.

Evidence of underlying symmetry and integrability in the quantum theory.

Abstract

We push forward the investigation of holographic dualities in 3D quantum gravity formulated as a topological quantum field theory, studying the correspondence between boundary and bulk structures. Working with the Ponzano-Regge topological state-sum model defining an exact discretization of 3d quantum gravity, we analyze how the partition function for a solid twisted torus depends on the boundary quantum state. This configuration is relevant to the AdS${}_{3}$/CFT${}_{2}$ correspondence. We introduce boundary spin network states with coherent superposition of spins on a square lattice on the boundary surface. This allows for the first exact analytical calculation of Ponzano-Regge amplitudes with extended 2D boundary (beyond the single tetrahedron). We get a regularized finite truncation of the BMS character formula obtained from the one-loop perturbative quantization of 3D gravity. This hints towards the existence of an underlying symmetry and the integrability of the theory for finite boundary at the quantum level for coherent boundary spin network states.