3d gravity as a random ensemble

A bstract We give further evidence that the matrix-tensor model studied in [1] is dual to AdS 3 gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT 2 data sub...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2025; no. 2; pp. 208 - 71
Main Authors Jafferis, Daniel L., Rozenberg, Liza, Wong, Gabriel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 28.02.2025
Springer Nature B.V
SpringerOpen
Subjects
AdS-CFT Correspondence
Black holes
Classical and Quantum Gravitation
Combinatorial analysis
Eigenvalues
Elementary Particles
Gravity
Hamiltonian functions
High energy physics
Manifolds (mathematics)
Matrix Models
Models of Quantum Gravity
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Tensors
Topological Field Theories
Topology
AdS-CFT Correspondence
Topological Field Theories
Matrix Models
Models of Quantum Gravity
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Summary:A bstract We give further evidence that the matrix-tensor model studied in [1] is dual to AdS 3 gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT 2 data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all 3-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with Virasoro TQFT (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in [1], the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT’s. We show how the SD equations can be translated into a combinatorial problem about 3-manifolds.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2025)208