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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2509.26052 |
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| _version_ | 1866909816606162944 |
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| author | Angelinos, Nikolaos |
| author_facet | Angelinos, Nikolaos |
| contents | We construct a model of 3D quantum gravity based on abelian topological quantum field theory (TQFT), by defining the gravitational path-integral as a sum over all 3D topologies with genus-$g$ boundary $Σ_g$. The path-integral of an abelian TQFT $\mathcal T$ on any single topology with boundary $Σ_g$ prepares a stabilizer state. This way, $\mathcal T$ partitions all these topologies into finitely many equivalence classes, where each topology within a class is associated with the same stabilizer state. The gravitational path-integral can thus be rephrased as a weighted sum over representative topologies, which are further organized into orbits under the mapping class group of $Σ_g$. One orbit is represented by handlebodies, whose average reproduces the ``Poincaré series of the vacuum", while additional orbits describe non-handlebody topologies. The resulting quantum gravity state is $Sp(2g,\mathbb Z)$-invariant and can be expressed as a weighted average of 2D CFT partition functions on $Σ_g$. This establishes a duality between a weighted sum over bulk topologies and a weighted sum over boundary CFTs. We introduce the ``$λ$-matrix", which relates bulk and boundary weights. The $λ$-matrix can be fully determined by the set of topological boundary conditions that the TQFT admits, and we present a systematic procedure to construct this set. Using this framework, we evaluate the $λ$-matrix and the TQFT gravity state in several tractable examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abelian 3D TQFT gravity, ensemble holography and stabilizer states Angelinos, Nikolaos High Energy Physics - Theory We construct a model of 3D quantum gravity based on abelian topological quantum field theory (TQFT), by defining the gravitational path-integral as a sum over all 3D topologies with genus-$g$ boundary $Σ_g$. The path-integral of an abelian TQFT $\mathcal T$ on any single topology with boundary $Σ_g$ prepares a stabilizer state. This way, $\mathcal T$ partitions all these topologies into finitely many equivalence classes, where each topology within a class is associated with the same stabilizer state. The gravitational path-integral can thus be rephrased as a weighted sum over representative topologies, which are further organized into orbits under the mapping class group of $Σ_g$. One orbit is represented by handlebodies, whose average reproduces the ``Poincaré series of the vacuum", while additional orbits describe non-handlebody topologies. The resulting quantum gravity state is $Sp(2g,\mathbb Z)$-invariant and can be expressed as a weighted average of 2D CFT partition functions on $Σ_g$. This establishes a duality between a weighted sum over bulk topologies and a weighted sum over boundary CFTs. We introduce the ``$λ$-matrix", which relates bulk and boundary weights. The $λ$-matrix can be fully determined by the set of topological boundary conditions that the TQFT admits, and we present a systematic procedure to construct this set. Using this framework, we evaluate the $λ$-matrix and the TQFT gravity state in several tractable examples. |
| title | Abelian 3D TQFT gravity, ensemble holography and stabilizer states |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.26052 |