Holographic Krylov Complexity for Conformal Quiver Gauge Theories

TL;DR

This work provides the first systematic study of holographic Krylov complexity in fully top-down AdS3 and AdS2 backgrounds dual to linear-quiver SCFTs and conformal quantum mechanics. By allowing warp factors to depend on a quiver coordinate η, the holographic geodesic probes both the radial AdS direction and the quiver direction, yielding quiver-dependent contributions to the rate of complexity growth. Across Abelian and non-Abelian T-duals and both localized and smeared flavor structures, the authors show that η-motion is UV-damped, imprinting early-time corrections that fade into universal late-time AdS behavior. The results establish a concrete holographic mechanism by which complexity encodes UV quiver data and IR universality, and they chart a path for extending Krylov complexity analyses to richer, multi-dimensional quiver geometries.

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 $η$ in this paper). This $η$-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 $η$-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 $η$-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.

Figures (16)

• Figure 1: A generic quiver field theory whose IR is dual to the holographic background defined by the functions in \ref{['profileh4sp']}-\ref{['profileh8sp']}. The solid horizontal black line represents a $(4,4)$ twisted-hypermultiplet connecting two nearest neighbor gauge nodes. Vertically two adjacent gauge nodes are connected by $(0,4)$ hypers represented by wiggly lines and diagonally by $(0,2)$ Fermi multiplets represented by dashed lines. The solid curved lines represent ${\cal N}=(4,4)$ twisted hypers, connecting flavour nodes with opposite gauge nodes.
• Figure 2: Hanany-Witten set-up associated with our generic quiver in figure \ref{['figurageneral']}. The vertical lines denote NS five branes, horizontal lines D2 and D6 colour branes. The crosses, D4 and D8 flavour branes.
• Figure 3: Quiver associated to the NATD solution.
• Figure 4: The particle trajectory along the $\eta$ direction for non-Abelian T-dual background. We set $\lambda=\mu=\nu=u_0=1$, $H_0=100$, $\eta_0=6$ and $e^{\lambda r_{UV}}=0.00024$ is fixed by the constraint \ref{['e3.25']}.
• Figure 5: Proper momentum $P_{\bar{\rho}}$ and its comparison with pure AdS case. $P_{\text{AdS}}$ is obtained by freezing the motion in the $\eta$-direction, as indicated below eq.(\ref{['eq:quivermomentum']}). We set $\mu=\nu=u_0=1, H_0=100$, and $\eta_0=6$.