Krylov Complexity, Confinement and Universality

TL;DR

This paper investigates Krylov complexity in confining quantum field theories using holographic duals, revealing universal oscillatory behavior linked to confinement scales, and compares these findings with the Ising model.

Contribution

It introduces a holographic geometric method to analyze Krylov complexity in confining theories and uncovers universal oscillatory patterns as signatures of confinement.

Findings

Krylov complexity oscillates in confining geometries.

Oscillation frequency relates to the confinement scale.

Qualitative agreement with the Ising model results.

Abstract

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a massive probe, we analyse radial geodesics in several top-down gravity duals exhibiting confinement and a mass gap. In all geometries with a smooth infrared end-of-space we uncover a robust and universal qualitative feature: Krylov complexity exhibits oscillatory behaviour. The oscillation frequency is controlled by the confinement scale, while the amplitude depends on both the ultraviolet cutoff and the infrared scale. Additional conserved charges modify these patterns without altering their qualitative structure. We further compare our results with the Krylov complexity of the longitudinally perturbed Ising model. The qualitative agreement suggests that oscillatory behaviour of Krylov complexity constitutes a universal signature of confinement and provides a sensitive probe of infrared reorganisation in strongly coupled quantum field theories.