Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena

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.

Section: Jhep01(2022)013mentioning

confidence: 99%

Chaos and pole-skipping in rotating black holes

Blake

Davison

2022

“…However, unlike the energy density two point function, the pole-skipping in other cases turned out not to be related to chaos. See also recent developments of pole-skipping in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

Jeong

Kim

Sun

2021

Self Cite

We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent (λL) and butterfly velocity (vB), independently of the symmetry breaking patterns. We show that the diffusion constant (D) is bounded by $$ D\ge {v}_B^2/{\lambda}_L $$ D ≥ v B 2 / λ L , where D is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.

“…Even though we do not know their exact expressions, we may determine the asymptotic behaviors of the half-geodesic Witten diagrams in general black holes by analyzing the asymptotic behaviors of the bulk-to-bulk propagators from the classical equations. In fact, the Lyapunov exponent and the butterfly velocity of theories with Einstein gravity duals in a large class of black holes were studied in [48,49], and similar analysis for the scalar and vector exchange was done in [50]. We note that the butterfly velocity in planar black holes depends on higher derivative couplings [31].…”

Section: Similarities With Other Holographic Computationsmentioning

confidence: 82%

Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena

Kim

Lee

Nishida

2021

Self Cite

We study a holographic construction of conformal blocks in the Regge limit of four-point scalar correlation functions by using coordinates of the two-sided Rindler-AdS black hole. As a generalization of geodesic Witten diagrams, we construct diagrams with four external scalar fields in the Rindler-AdS black hole by integrating over two half-geodesics between the centers of Penrose diagrams and points at the AdS boundary. We demonstrate that late-time behaviors of the diagrams coincide with the Regge behaviors of conformal blocks. We also point out their relevance with the pole-skipping phenomena by showing that the near-horizon analysis of symmetric traceless fields with any integer spin in the Rindler-AdS black hole can capture the Regge behaviors of conformal blocks.