Krylov Complexity, Confinement and Universality

Abstract

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a massive probe, we analyse radial geodesics in several top-down gravity duals exhibiting confinement and a mass gap. In all geometries with a smooth infrared end-of-space we uncover a robust and universal qualitative feature: Krylov complexity exhibits oscillatory behaviour. The oscillation frequency is controlled by the confinement scale, while the amplitude depends on both the ultraviolet cutoff and the infrared scale. Additional conserved charges modify these patterns without altering their qualitative structure. We further compare our results with the Krylov complexity of the longitudinally perturbed Ising model. The qualitative agreement suggests that oscillatory behaviour of Krylov complexity constitutes a universal signature of confinement and provides a sensitive probe of infrared reorganisation in strongly coupled quantum field theories.

Figures (10)

• Figure 1: $z(t)$ trajectory for various values of $Q$ and comparison with the AdS case.
• Figure 2: $P_{\bar{y}}(t)$ (upper panel) for $H=10$ and $C(t)$ (lower panel) for various values of $H$.
• Figure 3: $r(t)$, $C(t)$ and $C(t)$ with rescaled time. The calculation results for $J=0$(Green), $J=5$(Blue), and $J=9.5$(Orange) are depicted with $H=10$. The rescaling is done such that the frequency of the oscillations matches for different values of J.
• Figure 4: $C(t)$ with rescaled time for different J values and $H=10$ in early times (upper panel) and late times (lower panel). The rescaling is done such that the frequency of the oscillations match for different values of J
• Figure 5: $r(t)$, $P_{y}$ and $C(t)$ for D4 branes on $S^1$ with $r_\Lambda=1, N_c=10$ and $H=10$.