Bounding the Space of Holographic CFTs with Chaos

Perlmutter, Eric

doi:10.1007/JHEP10(2016)069

Bounding the Space of Holographic CFTs with Chaos

Eric Perlmutter
(
- Princeton U.
)

Feb 26, 2016

66 pages

Published in:

JHEP 10 (2016) 069

Published: Oct 13, 2016

e-Print:

1602.08272 [hep-th]

DOI:

10.1007/JHEP10(2016)069

View in:

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Abstract: (Springer)

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.

Note:

50+18 pages. v3: Section 3 clarified and reorganized, related improvements

AdS-CFT Correspondence
Conformal and W Symmetry
Higher Spin Gravity
field theory: conformal
spin: high
gravitation: higher-dimensional
n-point function: 4
duality: holography
operator product expansion
Lyapunov exponent

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