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Effective description of sub-maximal chaos: stringy effects for SYK scrambling

Effective description of sub-maximal chaos: stringy effects for SYK scrambling
Effective description of sub-maximal chaos: stringy effects for SYK scrambling
It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.
1126-6708
Haehl, Felix
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Mezei, Mark
cc925f3c-006f-4cbc-87cb-5ec618f90a17
Choi, Changha
e0dbd3a2-0bb5-4bbd-87de-614ab514f0bb
Sarosi, Gabor
587d5830-6341-4982-9d04-153718bc2900
Haehl, Felix
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Mezei, Mark
cc925f3c-006f-4cbc-87cb-5ec618f90a17
Choi, Changha
e0dbd3a2-0bb5-4bbd-87de-614ab514f0bb
Sarosi, Gabor
587d5830-6341-4982-9d04-153718bc2900

Haehl, Felix, Mezei, Mark, Choi, Changha and Sarosi, Gabor (2023) Effective description of sub-maximal chaos: stringy effects for SYK scrambling. Journal of High Energy Physics, [142].

Record type: Article

Abstract

It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

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JHEP03(2023)142 - Version of Record
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Accepted/In Press date: 10 March 2023
Published date: 21 March 2023

Identifiers

Local EPrints ID: 476688
URI: http://eprints.soton.ac.uk/id/eprint/476688
ISSN: 1126-6708
PURE UUID: 99bff8bc-6660-457c-88b9-dcf4ca642ecf
ORCID for Felix Haehl: ORCID iD orcid.org/0000-0001-7426-0962

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Date deposited: 11 May 2023 16:43
Last modified: 17 Mar 2024 04:14

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Contributors

Author: Felix Haehl ORCID iD
Author: Mark Mezei
Author: Changha Choi
Author: Gabor Sarosi

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