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

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.

arXiv comment44 pages

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• Spinfoams: Foundations
• The Quantum Gravity Disk: Discrete Current Algebra
• Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
• 3d Quantum Gravity Partition Function at 3 Loops: a brute force computation
• The Ponzano-Regge cylinder and Propagator for 3d quantum gravity
• 3D Quantum Gravity from Holomorphic Blocks
• Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
• Canonical description of Exotic General Massive Gravity
• The massive BMS character in 3D quantum gravity
• Hessian in the spinfoam models with cosmological constant