Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography

Hyun-Sik Jeong

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arXiv · 2602.11627

Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography

Hyun-Sik Jeong

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Abstract

We establish a holographic gravitational dual for the fundamental dynamical equations governing operator growth in Krylov subspace. Specifically, we show that the deep interior of the Krylov subspace maps directly to the near-horizon regime of AdS$_2$ gravity. We demonstrate that, in the continuum limit, the discrete evolution on the Krylov chain transforms into the dynamics of a continuous field, which is isomorphic to the Klein-Gordon equation for a scalar field in the AdS$_2$ throat. This correspondence identifies the linear growth rate of Lanczos coefficients with the Hawking temperature, $\alpha=\pi T$, thereby recovering the saturation of the maximal chaos bound. Notably, the Breitenlohner-Freedman bound, a fundamental stability criterion in AdS gravity, emerges as a necessary consistency requirement for the dual description of Krylov subspace dynamics. Our results advance a Krylov-based holographic dictionary in a unified $SL(2, \mathbb{R})$ representation, revealing that the emergent geometry of Krylov subspace is a reflection of the near-horizon AdS spacetime.

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Hyun-Sik Jeong. 2026-02-12. Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography. https://arxiv.org/abs/2602.11627

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