Holographic Krylov complexity in confining gauge theories

TL;DR

This paper investigates holographic Krylov complexity in a confining gauge theory using a top-down Type IIB background, revealing oscillatory behavior linked to UV cutoff and IR end-of-space, and providing insights into confining holographic dynamics.

Contribution

It offers the first analytic solutions for holographic Krylov complexity in a confining background, confirming the spread-momentum correspondence and highlighting differences from conformal cases.

Findings

Proper momentum and complexity oscillate due to UV cutoff and IR end-of-space.

Analytic solutions for radial geodesics are expressed with elliptic functions.

The study demonstrates qualitative differences between confining and conformal holographic dynamics.

Abstract

We study holographic Krylov complexity in the Anabalon-Ross solitonic background, a top-down Type IIB solution describing a twisted-circle compactification of ${\cal N}=4$ SYM that flows to a confining, gapped three-dimensional theory. Following the proposal that the time derivative of Krylov complexity is dual to the proper radial momentum of a falling bulk particle, we analyze probe geodesics in this geometry. We obtain exact analytic solutions for the radial trajectory in terms of elliptic functions, confirming and extending UV and IR asymptotic expansions. The proper momentum and resulting complexity exhibit oscillatory behaviour, which we interpret as a holographic signature of the finite Hilbert-space truncation induced by the UV cutoff together with the IR end-of-space. Our results provide a controlled top-down test of the spread-momentum correspondence and highlight qualitative differences between conformal and confining holographic dynamics.