Bounding the space of holographic CFTs with chaos

Perlmutter, Eric

doi:10.1007/JHEP10(2016)069

Title: Bounding the space of holographic CFTs with chaos

Journal Article · Thu Oct 13 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2016)069· OSTI ID:1362022

Perlmutter, Eric ^[1]

Princeton Univ., Princeton, NJ (United States)

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 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: λ_L = 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.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-91ER40671

OSTI ID:: 1362022

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 10; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 97 works

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Holographic Reconstruction of AdS Exchanges from Crossing Symmetry Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric arXiv https://doi.org/10.48550/arxiv.1705.02318	text	January 2017
Conformal Bootstrap in the Regge Limit Li, Daliang; Meltzer, David; Poland, David arXiv https://doi.org/10.48550/arxiv.1705.03453	text	January 2017
Operator bases, $S$-matrices, and their partition functions Henning, Brian; Lu, Xiaochuan; Melia, Tom arXiv https://doi.org/10.48550/arxiv.1706.08520	text	January 2017
Constraints on Higher Spin CFT$_2$ Afkhami-Jeddi, Nima; Colville, Kale; Hartman, Thomas arXiv https://doi.org/10.48550/arxiv.1707.07717	text	January 2017
Chaos and random matrices in supersymmetric SYK Hunter-Jones, Nicholas; Liu, Junyu arXiv https://doi.org/10.48550/arxiv.1710.08184	text	January 2017
Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks Kusuki, Yuya; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.1711.09913	text	January 2017
Supersymmetric SYK Model with Global Symmetry Narayan, Prithvi; Yoon, Junggi arXiv https://doi.org/10.48550/arxiv.1712.02647	text	January 2017
A Conformal Collider for Holographic CFTs Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein arXiv https://doi.org/10.48550/arxiv.1805.07393	text	January 2018
Effects of quintessence dark energy on the action growth and butterfly velocity Ghaffarnejad, Hossein; Farsam, Mohammad; Yaraie, Emad arXiv https://doi.org/10.48550/arxiv.1806.05735	text	January 2018
A Crossing-Symmetric OPE Inversion Formula Mazac, Dalimil arXiv https://doi.org/10.48550/arxiv.1812.02254	text	January 2018
Entanglement and chaos in warped conformal field theories Apolo, Luis; He, Song; Song, Wei arXiv https://doi.org/10.48550/arxiv.1812.10456	text	January 2018
Chaos bound in Bershadsky-Polyakov theory David, Justin R.; Hollowood, Timothy J.; Khetrapal, Surbhi arXiv https://doi.org/10.48550/arxiv.1906.00667	text	January 2019

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