Approximate CFTs and Random Tensor Models

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Belin, Alexandre, de Boer, Jan, Jafferis, Daniel Louis, Nayak, Pranjal, Sonner, Julian
Natura: Preprint
Pubblicazione: 2023
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866911865750159360
author Belin, Alexandre
de Boer, Jan
Jafferis, Daniel Louis
Nayak, Pranjal
Sonner, Julian
author_facet Belin, Alexandre
de Boer, Jan
Jafferis, Daniel Louis
Nayak, Pranjal
Sonner, Julian
contents A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of `CFT data'. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of `CFT data' satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS$_3$ as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.
format Preprint
id arxiv_https___arxiv_org_abs_2308_03829
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Approximate CFTs and Random Tensor Models
Belin, Alexandre
de Boer, Jan
Jafferis, Daniel Louis
Nayak, Pranjal
Sonner, Julian
High Energy Physics - Theory
Strongly Correlated Electrons
General Relativity and Quantum Cosmology
A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of `CFT data'. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of `CFT data' satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS$_3$ as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.
title Approximate CFTs and Random Tensor Models
topic High Energy Physics - Theory
Strongly Correlated Electrons
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2308.03829