# Horizon constraints on holographic Green's functions

## TL;DR

This paper investigates how near-horizon behavior in holographic models constrains the properties of Green's functions, revealing pole-skipping phenomena that impact collective mode dispersion and have implications for transport and chaos.

## Contribution

It introduces a new class of properties of holographic Green's functions derived from near-horizon analysis, highlighting pole-skipping points and their effects on boundary theory dynamics.

## Key findings

- Identification of pole-skipping points at negative imaginary Matsubara frequencies.
- Demonstration of how dispersion relations of hydrodynamic modes pass through pole-skipping points.
- Implications for understanding transport, hydrodynamics, and quantum chaos in holographic systems.

## Abstract

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 $\omega\sim T$ 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.