Bounding the space of holographic CFTs with chaos

• Published in: The journal of high energy physics Vol. 2016; no. 10; pp. 1 - 60
• Main Author: Perlmutter, Eric
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016; Springer Nature B.V; Springer Berlin
• Subjects: AdS-CFT correspondence; Chaos theory; Classical and Quantum Gravitation; conformal and W symmetry; Coupling; Degrees of freedom; Elementary Particles; Gravitation; Harnesses; High energy physics; higher spin gravity; Lyapunov exponents; Mathematical analysis; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Towers; Higher Spin Gravity; AdS-CFT Correspondence; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2016)069

A bstract 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 encourage a tensionless string theory interpretation of the 3D Vasiliev theory.