BTZ dynamics and chaos

Poojary, Rohan R.

doi:10.1007/jhep03(2020)048

Cited by 48 publications

(78 citation statements)

References 83 publications

(126 reference statements)

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“…For example, in a holographic 2d CFT, one can calculate the OTOC in a rotating ensemble, by repeating the Shenker-Stanford shockwave calculation [11,18,19] for rotating BTZ. This has been done in [20,21], and these authors concluded that the bound λ L ≤ 2π/β is not obeyed. We will re-examine these calculations and will reach a different conclusion.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…At strong coupling one has v * = 2/ √ λ 't Hooft [35,36,44], which is small as expected. 20 A cartoon of j(ν) along the imaginary axis is shown on Fig. 11, adapted from [36].…”

Section: Critical Velocity and Exchange Of Dominancementioning

confidence: 99%

“…19 The Regge trajectory at weak coupling in a neighborhood of the stress tensor, r = iν = 2 is given by j(r) = r − λ 't Hooft H(r − 2)/(2π 2 ) + O λ 2 't Hooft , where H(n) is the nth harmonic number. 20 The Regge trajectory at strong coupling is j(ν) = 2 − (4 + ν 2 )/(2 √ λ 't Hooft ) + O (1/λ 't Hooft ).…”

Section: Critical Velocity and Exchange Of Dominancementioning

confidence: 99%

“…Below we present the computation of the OTOC in a rotating thermal ensamble in a 2d CFT with an Einstein gravity dual. Most of the computations were done in [20,21,51]; the novelty of this section is a careful interpretation of the results and their comparison with other results in this paper.…”

Section: Otoc In a Rotating Black Holementioning

confidence: 99%

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Chaos in the butterfly cone

Mezei

Sárosi

2020

J. High Energ. Phys.

146

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A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/v B ), where T is the temperature and v B is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v * < v B . In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…At strong coupling one has v * = 2/ √ λ 't Hooft [35,36,44], which is small as expected. 20 A cartoon of j(ν) along the imaginary axis is shown on Fig. 11, adapted from [36].…”

Section: Critical Velocity and Exchange Of Dominancementioning

confidence: 99%

Section: Critical Velocity and Exchange Of Dominancementioning

confidence: 99%

Section: Otoc In a Rotating Black Holementioning

confidence: 99%

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Chaos in the butterfly cone

Mezei

Sárosi

2020

J. High Energ. Phys.

146

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“…The resulting 2D theory of gravity contains, in addition to the metric, a gauge field and a dilaton as expected in Kaluza-Klein theory. Our work builds upon the developments in [17,30], where the 2D holographic dictionary was studied by dimensionally reducing the 3D Einstein-Hilbert action with a negative cosmological constant.Other relevant work includes [31], which focuses on the effects of U (1) Chern-Simons fields in 2D; see also [22,[32][33][34][35].One question we investigate is the relation between the nCFT 1 , that describes the near horizon physics of near-extremal BTZ, to the parent CFT 2 , that is dual to AdS 3 . This relation is subtle:The conformal (Weyl) anomaly in AdS 3 /CFT 2 can easily be confused with the anomaly appearing…”

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confidence: 99%

Gravitational anomalies in nAdS₂/nCFT₁

Castro

Mühlmann

2020

Class. Quantum Grav.

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We revisit the holographic description of the near horizon geometry of the BTZ black hole in AdS3 gravity, with a gravitational Chern–Simons term included. After a dimensional reduction of the three dimensional theory, we use the framework of nAdS2/nCFT1 to describe the near horizon physics. This setup allows us to contrast the role of the gravitational and conformal anomaly inherited from AdS3/CFT2 in the symmetry breaking mechanism of nAdS2/nCFT1. Our results display how boundary conditions in the 3D spacetime, combined with the gravitational anomaly, affect the holographic description of the near horizon of the black hole relative to the physics near the AdS3 boundary.

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Horizon constraints on holographic Green’s functions

2020

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We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these 'pole-skipping' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales ω ∼ T are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U (1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole-skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems. arXiv:1904.12883v3 [hep-th] 13 Jan 2020 45 E.3 Transverse metric perturbations 48 E.4 Longitudinal metric perturbations 49 E.5 Transverse metric perturbations in a charged black hole 52 -1 -1 v B is the 'butterfly velocity' [15][16][17] of the dual quantum field theory. 2 Pole-skipping in G R εε at (ω * , k * ) was also shown to hold in holographic theories dual to higher derivative gravity in [20].3 The symbol ω n is more conventionally used to refer to the real set of Matsubara frequencies ω E = 2πT n at which the Euclidean Green's function is defined. Here we are interested in studying the real time correlator G R (ω, k) and will abuse the more common notation somewhat by using the symbol ω n to refer to the special pure imaginary frequencies ω = ω n = −i2πT n. These are referred to as the 'negative imaginary Matsubara frequencies' for obvious reasons.We are grateful to Nejc Ceplak, Saso Grozdanov, Hong Liu, and Andrei Starinets for helpful discussions. M. B. received support from the Office of High Energy Physics of U.S.

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BTZ dynamics and chaos

Cited by 48 publications

References 83 publications

Chaos in the butterfly cone

Chaos in the butterfly cone

Gravitational anomalies in nAdS₂/nCFT₁

Horizon constraints on holographic Green’s functions

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BTZ dynamics and chaos

Cited by 48 publications

References 83 publications

Chaos in the butterfly cone

Chaos in the butterfly cone

Gravitational anomalies in nAdS2/nCFT1

Horizon constraints on holographic Green’s functions

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Gravitational anomalies in nAdS₂/nCFT₁