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Title: Bounding the space of holographic CFTs with chaos

In this study, thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ L ≤ 2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ L = 2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge and a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS 3 higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W [λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ L = 0. Independently, we show that such theories violate unitarity for |λ| > 2. These results encouragemore » a tensionless string theory interpretation of the 3D Vasiliev theory.« less
Authors:
 [1]
  1. Princeton Univ., Princeton, NJ (United States)
Publication Date:
Grant/Contract Number:
FG02-91ER40671
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
The Trustees of Princeton Univ., Princeton, NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; conformal and W symmetry; higher spin gravity
OSTI Identifier:
1362022

Perlmutter, Eric. Bounding the space of holographic CFTs with chaos. United States: N. p., Web. doi:10.1007/JHEP10(2016)069.
Perlmutter, Eric. Bounding the space of holographic CFTs with chaos. United States. doi:10.1007/JHEP10(2016)069.
Perlmutter, Eric. 2016. "Bounding the space of holographic CFTs with chaos". United States. doi:10.1007/JHEP10(2016)069. https://www.osti.gov/servlets/purl/1362022.
@article{osti_1362022,
title = {Bounding the space of holographic CFTs with chaos},
author = {Perlmutter, Eric},
abstractNote = {In this study, thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λL ≤ 2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λL = 2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge and a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS3 higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W∞[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λL = 0. Independently, we show that such theories violate unitarity for |λ| > 2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.},
doi = {10.1007/JHEP10(2016)069},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2016,
place = {United States},
year = {2016},
month = {10}
}