Pole-skipping as missing states

TL;DR

This paper investigates pole-skipping phenomena in the AdS soliton background, revealing how it affects the normal mode spectrum and explains missing states as a physical signature of pole-skipping.

Contribution

It demonstrates that pole-skipping occurs in the AdS soliton and explains the missing states in the spectrum as a consequence of pole-skipping points.

Findings

Pole-skipping appears in the AdS soliton background.

Missing states in the spectrum are explained by pole-skipping.

The spectrum's puzzling features are resolved by considering pole-skipping points.

Abstract

It remains unclear in general how the pole-skipping appears as a physical phenomenon, and we study the issue in the context of the AdS soliton. The pole-skipping has been discussed in black hole backgrounds, but the pole-skipping occurs even in the AdS soliton background. The geometry has a compact $S^1$-direction, and we compute the mass spectrum for the bulk scalar field, the bulk Maxwell field, and the gravitational perturbations with $S^1$ momentum. We show that the pole-skipping leaves its fingerprint in the the normal mode spectrum. The spectrum has some puzzling features because the would-be states are missing at pole-skipping points. The puzzling features disappear once one takes into account these pole-skipping points that we call "missing states."