dorsal/arxiv
View SchemaA universal sum over topologies in 3d gravity
| Authors | Alexandre Belin, Scott Collier, Lorenz Eberhardt, Diego Liska, Boris Post |
|---|---|
| Categories | |
| ArXiv ID | 2601.07906vv1 |
| URL | https://arxiv.org/abs/2601.07906 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We explore the sum over topologies in AdS$_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal statistical properties of high-energy CFT$_2$ data. We identify a series of surgery moves on bulk manifolds that precisely reflect the requirements of typicality and crossing symmetry of the boundary ensemble. These surgery moves generate a large number of bulk manifolds that have to be included in any reasonable definition of the gravitational path integral. We show that this procedure generates only on-shell (hyperbolic) manifolds, although it does not produce all of them. These proofs rely on structure theorems of 3-manifolds, which non-trivially interact with the requirements of the statistical boundary ensemble. We illustrate the application of this procedure with many examples, such as Euclidean wormholes, twisted $I$-bundles and handlebody-knots. Our findings reveal a large space of possible choices of which manifolds can be included in the gravitational path integral, reflecting a wide range of possible statistical ensembles consistent with crossing symmetry and typicality.
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"abstract": "We explore the sum over topologies in AdS$_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal statistical properties of high-energy CFT$_2$ data. We identify a series of surgery moves on bulk manifolds that precisely reflect the requirements of typicality and crossing symmetry of the boundary ensemble. These surgery moves generate a large number of bulk manifolds that have to be included in any reasonable definition of the gravitational path integral. We show that this procedure generates only on-shell (hyperbolic) manifolds, although it does not produce all of them. These proofs rely on structure theorems of 3-manifolds, which non-trivially interact with the requirements of the statistical boundary ensemble. We illustrate the application of this procedure with many examples, such as Euclidean wormholes, twisted $I$-bundles and handlebody-knots. Our findings reveal a large space of possible choices of which manifolds can be included in the gravitational path integral, reflecting a wide range of possible statistical ensembles consistent with crossing symmetry and typicality.",
"arxiv_id": "2601.07906",
"authors": [
"Alexandre Belin",
"Scott Collier",
"Lorenz Eberhardt",
"Diego Liska",
"Boris Post"
],
"categories": [
"hep-th",
"math-ph",
"math.MP"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A universal sum over topologies in 3d gravity",
"url": "https://arxiv.org/abs/2601.07906",
"version": "v1"
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