Non-perturbative 3D quantum gravity: quantum boundary states and exact partition function

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 quant...

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Bibliographic Details
Published in:General relativity and gravitation 2020, Vol.52 (3), Article 24
Main Authors: Goeller, Christophe, Livine, Etera R., Riello, Aldo
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Differential Geometry
Editor’s Choice (Research Article)
Field theory
Gravity
Mathematical and Computational Physics
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum field theory
Quantum gravity
Quantum Physics
Quantum theory
Relativity Theory
Tetrahedra
Theoretical
Three dimensional models
Topology
Toruses
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Summary: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 analyse 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.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-020-02673-3