Holographic Krylov Complexity for Conformal Quiver Gauge Theories

TL;DR

This paper explores how holographic Krylov complexity behaves in top-down AdS$_3$ and AdS$_2$ supergravity backgrounds dual to 2D and 1D conformal theories, revealing new quiver-dependent effects and late-time universal growth patterns.

Contribution

It introduces the study of Krylov complexity in top-down holographic models with non-trivial quiver structures, highlighting the impact of quiver dynamics on complexity growth.

Findings

Quiver coordinate motion affects complexity growth rates.

Late-time complexity growth becomes universal, matching pure AdS predictions.

Quiver parameters influence early-time operator-spreading dynamics.

Abstract

We investigate holographic Krylov complexity in fully top-down AdS$_3$ and AdS$_2$ supergravity backgrounds dual to two-dimensional linear-quiver SCFTs and one-dimensional conformal quantum mechanics. In these geometries, the warp factors, dilaton and other fields depend non-trivially on the 'quiver coordinate' (denoted by $\eta$ in this paper). This $\eta$-coordinate encodes the color and flavor data of the dual theories. As a consequence, a massive probe following a holographic geodesic necessarily moves simultaneously in the radial AdS direction and along the 'quiver direction'. This produces new contributions to the proper momentum and hence to the rate of Krylov complexity growth, which is absent in bottom-up AdS models. We show that the $\eta$-motion is generically damped, with a time-scale governed by the UV cutoff of the geodesic problem, and modifies the early-time evolution of complexity in a quiver-dependent way. At late times, the $\eta$-dynamics freezes and the growth becomes universal, matching pure Poincare AdS predictions. Studying Abelian and non-Abelian T-dual backgrounds of AdS$_3\times S^3\times T^4$, quivers with localized flavor groups, and quivers with smeared flavor groups, we quantify how quiver parameters shape the operator-spreading dynamics. Our results provide a systematic characterization of Krylov complexity in top-down AdS$_3$/AdS$_2$ duals and reveal a holographic mechanism through which complexity probes both ultraviolet quiver structure and emergent infrared universality.