# Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

@article{Ahn2020PoleskippingOS, title={Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography}, author={Yongjun Ahn and Viktor Jahnke and Hyun-Sik Jeong and Keun-Young Kim and Kyungsun Lee and Mitsuhiro Nishida}, journal={arXiv: High Energy Physics - Theory}, year={2020} }

Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in $d$-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping…

## 22 Citations

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## References

SHOWING 1-10 OF 66 REFERENCES

Fermionic pole-skipping in holography

- Physics
- 2019

We examine thermal Green’s functions of fermionic operators in quantum field theories with gravity duals. The calculations are performed on the gravity side using ingoing Eddington-Finkelstein…

Holographic chaos, pole-skipping, and regularity

- MathematicsProgress of Theoretical and Experimental Physics
- 2020

We investigate the “pole-skipping” phenomenon in holographic chaos. According to pole-skipping, the energy-density Green’s function is not unique at a special point in the complex momentum plane.…

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory.

- PhysicsPhysical review letters
- 2015

Chaos dynamics in two-dimensional conformal field theory is studied through out-of-time-order thermal correlators of the form ⟨W (t)VW(t)V⟩ by studying the large c Virasoro identity conformal block.

Two-dimensional conformal field theory and the butterfly effect

- Physics
- 2014

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form 〈W (t)VW (t)V 〉. We reproduce bulk calculations similar to those of [1],…

Nonuniqueness of Green’s functions at special points

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We investigate a new property of retarded Green’s functions using AdS/CFT. The Green's functions are not unique at special points in complex momentum space. This arises because there is…

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

- PhysicsJournal of High Energy Physics
- 2019

A bstractPole-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 complex life of hydrodynamic modes

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We study analytic properties of the dispersion relations in classical hydrody- namics by treating them as Puiseux series in complex momentum. The radii of convergence of the series are…

Spinning conformal correlators

- Computer Science
- 2011

A bstractWe develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an indexfree notation where tensors…

Bounding the space of holographic CFTs with chaos

- Physics
- 2016

A bstractThermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λL ≤ 2π/β. We harness this…