Constraints on quasinormal modes and bounds for critical points from pole-skipping

TL;DR

This paper explores the relationship between pole-skipping points, quasinormal modes, and critical points in holographic thermal states, revealing bounds and transitions that deepen understanding of non-hydrodynamic modes.

Contribution

It introduces a novel analysis linking pole-skipping points with quasinormal modes and critical points, including bounds on convergence radii and class transitions based on operator dimensions.

Findings

Pole-skipping points constrain quasinormal mode dispersion relations.

Convergence radii of derivative expansions are bounded by pole-skipping points.

A transition between classes of critical points occurs at a specific conformal dimension.

Abstract

We consider a holographic thermal state and perturb it by a scalar operator whose associated real-time Green's function has only gapped poles. These gapped poles correspond to the non-hydrodynamic quasinormal modes of a massive scalar perturbation around a Schwarzschild black brane. Relations between pole-skipping points, critical points and quasinormal modes in general emerge when the mass of the scalar and hence the dual operator dimension is varied. First, this novel analysis reveals a relation between the location of a mode in the infinite tower of quasinormal modes and the number of pole-skipping points constraining its dispersion relation at imaginary momenta. Second, for the first time, we consider the radii of convergence of the derivative expansions about the gapped quasinormal modes. These convergence radii turn out to be bounded from above by the set of all pole-skipping points. Furthermore, a transition between two distinct classes of critical points occurs at a particular value for the conformal dimension, implying close relations between critical points and pole-skipping points in one of those two classes. We show numerically that all of our results are also true for gapped modes of vector and tensor operators.