Chaos, diffusivity, and spreading of entanglement in magnetic branes, and the strengthening of the internal interaction

Pedraza

2018

Self Cite

Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, N " 4 non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non-commutative parameter θ, however, both the butterfly and entanglement velocities increase with the strength of the noncommutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory. We comment on a possible limitation on the retrieval of quantum information imposed by non-locality. arXiv:1808.10050v3 [hep-th] 15 Nov 2018 6 Conclusions and outlook 34 A Momentum space correlator and the butterfly velocity 36 B Shock wave parameter α as a function of r 0 38 C Divergence of K 3 pr 0 q 39 -1 -

Section: Chaos and Entanglement Spreadingmentioning

confidence: 99%

Chaos and entanglement spreading in a non-commutative gauge theory

Fischler

Pedraza

2018

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“…We think this violation occurs because the rotation breaks the Z 2 isometry of the non-rotating geometry, and this introduces an asymmetry between the left and right moving modes in the co-rotating frame. This is reminiscent of the cases studied in [76][77][78], where the breaking of rotational symmetry caused the violation of a different (and more strong) bound for the butterfly velocity. Finally, we note that, at r − = 0, we should recover the Rindler AdS 3 result of S&S [9] by taking the limit β/ << 1 and φ << 1 of our results 12 .…”

Section: Co-rotating Framementioning

confidence: 86%

On the chaos bound in rotating black holes

Kim

Yoon

2019

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118

We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two different approaches: the elastic eikonal gravity approximation, and the Chern-Simons formulations of 3-dimensional gravity. Within both methods the OTOC is given as a sum of two contributions, corresponding to left and right moving modes. The contributions have different Lyapunov exponents, λ ± L = 2π β 1 1∓ Ω , where Ω is the angular velocity and is the AdS radius. Since λ − L ≤ 2π β ≤ λ + L , there is an apparent contradiction with the chaos bound. We discuss how the result can be made consistent with the chaos bound if one views the parameters β ± = β(1 ∓ Ω) as the effective inverse temperatures of the left and right moving modes. arXiv:1903.09086v2 [hep-th] 12 Apr 2019Contents 1 These recent developments were reviewed in [4,5].

“…This bound was shown to be violated by anisotropy[40][41][42][43] and higher curvature corrections[37]. For…”

mentioning

confidence: 99%

Scrambling in hyperbolic black holes: shock waves and pole-skipping

Ahn

Jeong

et al. 2019

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We study the scrambling properties of (d + 1)-dimensional hyperbolic black holes. Using the eikonal approximation, we calculate out-of-time-order correlators (OTOCs) for a Rindler-AdS geometry with AdS radius , which is dual to a d−dimensional conformal field theory (CFT) in hyperbolic space with temperature T = 1/(2π ). We find agreement between our results for OTOCs and previously reported CFT calculations. For more generic hyperbolic black holes, we compute the butterfly velocity in two different ways, namely: from shock waves and from a pole-skipping analysis, finding perfect agreement between the two methods. The butterfly velocity v B (T ) nicely interpolates between the Rindler-AdS result v B (T = 1 2π ) = 1 d−1 and the planar result v B (T 1 ) = d 2(d−1) .arXiv:1907.08030v2 [hep-th]