Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
| Autor: | Goeller, Christophe, Oriti, Daniele, Schmid, Gabriel |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Annales Henri Poincar\'e (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00023-023-01330-0 |
| Popis: | We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity. Comment: 42+15 pages, 28+14 figures; revised version matching article published in Annales Henri Poincar\'e |
| Databáze: | arXiv |
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