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

Sašo Grozdanov

doi:10.1007/jhep01(2019)048

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 (R2) corrections and then type IIB supergravity theory with the α′ 3R4 term, where α′ is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order 1/Nc corrections (with Nc 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 α′ 3R4 deformation enables us to study perturbative inverse ’t Hooft coupling corrections (α′ 3 ∼ 1/λ3/2) in SU(Nc), mathcal{N}=4 supersymmetric Yang-Mills theory with infinite Nc. While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on Nc 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.

Highlights

JHEP01(2019)048 statement to date, by following the observation of [21] that the anomalous chiral magnetic conductivity can be computed from a horizon formula, ref. [22] proved the universality of four anomalous chiral conductivities to all orders in the inverse coupling expansion, i.e. in any classical higher-derivative bulk theory, given certain conditions specified in [22]
A new type of a universal statement connecting hydrodynamics to the underlying microscopic properties transpired from studies in holography and effective field theory [23,24,25]
We will refer to this point as the “point of chaos” because λL and vB are the Lyapunov exponent and the butterfly velocity of the underlying quantum chaotic dynamics normally computed by the out-of-time-ordered correlation function: C(t, x) ∼ eλL(t−|x|/vB)

Summary

Introduction

JHEP01(2019)048 statement to date, by following the observation of [21] that the anomalous chiral magnetic conductivity can be computed from a horizon formula, ref. [22] proved the universality of four anomalous chiral conductivities to all orders in the inverse coupling expansion, i.e. in any classical higher-derivative bulk theory, given certain conditions specified in [22]. We will extend the holographic discussions of [23] and [25] to examine whether the above-presented relation between hydrodynamics and quantum chaos can exist in the presence of stringy bulk corrections — i.e. in field theories at finite ’t Hooft coupling λ and finite Nc. In sections 2 and 3, we will show that to leading order in 1/Nc and inverse coupling, this is the case.

Results

Conclusion