Momentum-Krylov complexity correspondence

In this work, we relate the growth rate of Krylov complexity in the boundary to the radial momentum of an infalling particle in AdS geometry. We show that in general AdS black hole background, our proposal captures the universal behaviors of Krylov complexity at both initial and late times. Hence it can be generally considered as an approximate dual of the Krylov complexity at least in diverse dimensions. Remarkably, for BTZ black holes, our holographic Krylov complexity perfectly matches with that of CFT${}_2$ at finite temperatures.