A cordial introduction to double scaled SYK

Micha Berkooz; Ohad Mamroud

doi:10.1088/1361-6633/ada889

A cordial introduction to double scaled SYK

Micha Berkooz^*, Ohad Mamroud

^*Corresponding author for this work

Department of Particle Physics and Astrophysics

Research output: Contribution to journal › Review article › peer-review

2 Citations (Scopus)

Abstract

We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS₂. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS₂. We conclude with discussion of related universality classes, and survey some of the current research directions.

Original language	English
Article number	036001
Number of pages	26
Journal	Reports on Progress in Physics
Volume	88
Issue number	3
Early online date	14 Feb 2025
DOIs	https://doi.org/10.1088/1361-6633/ada889
Publication status	Published - 1 Mar 2025

Funding

We would like to thank A Almheiri, A Altland, A Blommaert, N Brukner, R Frumkin, F Haehl, M Isachenkov, Y Jia, P Narayan, V Narovlansky, A Raz, S Ross, M Rozali, J Seitz, J Simon and M Watababe for many useful discussions. OM is supported by the ERC-COG Grant NP-QFT No. 864583 'Non-perturbative dynamics of quantum fields: from new deconfined phases of matter to quantum black holes', by the MUR-FARE2020 Grant No. R20E8NR3HX 'The Emergence of Quantum Gravity from Strong Coupling Dynamics', and by the INFN 'Iniziativa Specifica GAST'. The work of MB is supported in part by the Israel Science Foundation Grant No. 2159/22, by the Minerva foundation, and by a German-Israeli Project Cooperation (DIP) grant "Holography and the Swampland". MB is an incumbent of the Charlesand David Wolfson Professorial Chair of Theoretical Physics.

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1088/1361-6633/ada889

https://arxiv.org/abs/2407.09396Licence: CC BY

Cite this

@article{a82bfcfb0d924baaadf1809a932e9fd2,

title = "A cordial introduction to double scaled SYK",

abstract = "We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS2. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS2. We conclude with discussion of related universality classes, and survey some of the current research directions.",

author = "Micha Berkooz and Ohad Mamroud",

note = "Publisher Copyright: {\textcopyright} 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.",

year = "2025",

month = mar,

day = "1",

doi = "10.1088/1361-6633/ada889",

language = "English",

volume = "88",

journal = "Reports on Progress in Physics",

issn = "0034-4885",

publisher = "Institute of Physics Publishing",

number = "3",

}

TY - JOUR

T1 - A cordial introduction to double scaled SYK

AU - Berkooz, Micha

AU - Mamroud, Ohad

PY - 2025/3/1

Y1 - 2025/3/1

N2 - We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS2. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS2. We conclude with discussion of related universality classes, and survey some of the current research directions.

AB - We review recent progress regarding the double scaled Sachdev-Ye-Kitaev model and other p-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and Lyapunov exponent. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS2. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS2. We conclude with discussion of related universality classes, and survey some of the current research directions.

UR - http://www.scopus.com/inward/record.url?scp=85217921742&partnerID=8YFLogxK

U2 - 10.1088/1361-6633/ada889

DO - 10.1088/1361-6633/ada889

M3 - Review article

AN - SCOPUS:85217921742

SN - 0034-4885

VL - 88

JO - Reports on Progress in Physics

JF - Reports on Progress in Physics

IS - 3

M1 - 036001

ER -

A cordial introduction to double scaled SYK

Abstract

Funding

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this