Bounding the space of holographic CFTs with chaos

By Eric Perlmutter. 2016

167 citations recorded by the source corpus.

A bstractThermal 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/226b8492b3de8d957ac0b689f21804c14143d5c2

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Citations in the corpus

The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “The special case of this formula where h0 = 0 was proven recently in [78], using hypergeometric function identities from [79].”
Loops in AdS from conformal field theory (2016, background): “Knowing loop amplitudes in a given bulk theory would open the door to nonplanar extensions of dynamical aspects of holography and the conformal bootstrap [34–50].”
Universal diffusion in incoherent black holes (2016, background): “As we argued in [8], one natural way to define such a velocity in a holographic theory is provided by the butterfly effect [9–18].”
Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “24 For the hyperbolic geometries considered here and the temperature T = 1 2πR , this velocity is given by [105, 106]”
Onset of many-body chaos in the $O(N)$ model (2017, unknown): “This is consistent with earlier arguments [66].”