Quantum Chaos in Topologically Massive Gravity

Liu, Yan; Raju, Avinash

doi:10.48550/arxiv.2005.08508

Cited by 6 publications

(9 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where λ L = 2πT is the Lyapunov exponent for holographic theories and v B is the butterfly velocity. Thus this location seems to be connected to the chaotic properties of holographic systems [12-14] 1 , which is the case even in the presence of stringy corrections [17] (see [18][19][20][21][22] for further examples).…”

Section: Introductionmentioning

confidence: 99%

Pole-skipping and Rarita-Schwinger fields

Ceplak,

Vegh

2021

Preprint

View full text Add to dashboard Cite

In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the 'pole-skipping' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from the origin being equal to half of the Lyapunov exponent for maximally chaotic theories.

show abstract

Section: Introductionmentioning

confidence: 99%

Pole-skipping and Rarita-Schwinger fields

Ceplak,

Vegh

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…One important exception is provided by the study of rotating BTZ black holes, which are dual to a 1+1 dimensional CFT on a circle with a chemical potential for rotation. 2 In such a setting, the form of the OTOC was studied in [53,54] (see also [55][56][57][58][59][60]), and in [61] it has been shown that a natural generalisation of pole-skipping applies for arbitrary values of rotation. Whilst the fact that pole-skipping continues to hold in this case is reassuring, and provides evidence that a hydrodynamic effective theory of chaos continues to apply, both the effects of rotation and the dual gravity description are particularly simple for 1+1 dimensional CFTs.…”

Section: Introductionmentioning

confidence: 99%

Chaos and pole-skipping in rotating black holes

Blake¹,

Davison²

2021

Preprint

View full text Add to dashboard Cite

We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency ω * = i2πT there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of "pole-skipping" -namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT. Contents 1 Introduction 1 2 The Kerr-AdS Black Hole 4 3 OTOCs in Kerr-AdS black holes 7 3.1 Equatorial OTOC in Kerr-AdS black holes 10 4 Near-horizon metric perturbations of Kerr-AdS 13 5 Pole-skipping and quasinormal modes in Kerr-AdS 15 5.1 The Teukolsky equations 16 5.2 Existence of extra ingoing modes 18 5.3 Quasinormal modes and pole-skipping 23 5.4 Equatorial OTOC and pole-skipping in the slowly rotating limit 25 6 Discussion 28 A Kerr-AdS metric in Kruskal-like coordinates 31 B Shock wave profile in slowly-rotating limit 32 C Additional details of Teukolsky formalism 33 D Explicit demonstration of existence of a quasinormal mode 35

show abstract

“…So the connection can be realized from the AdS/CFT correspondence. A list of several other works recently done on pole skipping phenomenon can be found in [31][32][33][34][35][36][37][38]. 2 In this paper we have considered a gravitational background with a spatial anisotropy as obtained in [40,41].…”

Section: Introductionmentioning

confidence: 99%

Pole skipping and chaos in anisotropic plasma: a holographic study

Sil

2020

Preprint

View full text Add to dashboard Cite

Recently, a direct signature of chaos in many body system has been realized from the energy density retarded Green's function using the phenomenon of 'pole skipping'. Moreover, special locations in the complex frequency and momentum plane are found, known as the pole skipping points such that the retarded Green's function can not be defined uniquely there. In this paper, we compute the correction/shift to the pole skipping points due to a spatial anisotropy in a holographic system by performing near horizon analysis of EOMs involving different bulk field perturbations, namely the scalar, the axion and the metric field. For vector and scalar modes of metric perturbations we construct the gauge invariant variable in order to obtain the master equation. Two separate cases for every bulk field EOMs is considered with the fluctuation propagating parallel and perpendicular to the direction of anisotropy. We compute the dispersion relation for momentum diffusion along the transverse direction in the shear channel and show that it passes through the first three successive pole skipping points. The pole skipping phenomenon in the sound channel is found to occur in the upper half plane such that the parameters Lyapunov exponent λ L and the butterfly velocity v B are explicitly obtained thus establishing the connection with many body chaos.

show abstract

Quantum Chaos in Topologically Massive Gravity

Cited by 6 publications

References 40 publications

Pole-skipping and Rarita-Schwinger fields

Pole-skipping and Rarita-Schwinger fields

Chaos and pole-skipping in rotating black holes

Pole skipping and chaos in anisotropic plasma: a holographic study

Contact Info

Product

Resources

About