On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections

Abstract

Pole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with higher-derivative gravity duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared ($R^2$) corrections and then type IIB supergravity theory with the ${\alpha }^{\prime 3}{R}^4$ term, where ${\alpha }^{\prime }$ is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order $1/N_c$ corrections (with $N_c$ being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The ${\alpha }^{\prime 3}{R}^4$ deformation enables us to study perturbative inverse 't Hooft coupling corrections (${\alpha }^{\prime 3}\sim 1/{\lambda }^{3/2}$) in $SU(N_c)$, $\mathcal{N}=4$ supersymmetric Yang-Mills theory with infinite $N_c$. While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on $N_c$ and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.

arXiv commentV2: 20 pages, 1 figure. References added. Version to appear in JHEP

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