Holographic Krylov complexity in ${\cal N}=4$ SYM

TL;DR

This paper introduces a holographic approach to Krylov complexity in ${ m extbf{N}=4}$ SYM, linking it to motion in $AdS_5$ sliced by $AdS_3$, and explores its relation to specific subsectors.

Contribution

It proposes a novel holographic calculation of Krylov complexity in ${ m extbf{N}=4}$ SYM using $AdS_5$-$AdS_3$ slicing, connecting geometric motion to quantum complexity.

Findings

Holographic Krylov complexity is computed via proper momentum in $AdS_5$.

Motion in $AdS_3$ corresponds to the $Sl(2)$ subsector complexity.

General motion relates to the full ${ m extbf{N}=4}$ SYM complexity.

Abstract

We propose and calculate a holographic Krylov complexity in ${\cal N}=4$ SYM via the proper momentum for motion in $AdS_5$ sliced by $AdS_3$. The motion in an $AdS_3$ subgroup corresponds to the Krylov complexity of the $Sl(2)$ subsector. The general motion corresponds to the Krylov complexity of the ${\cal N}=4$ SYM.