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

• URL: http://arxiv.org/abs/2602.11627v1
• Date: Thu, 12 Feb 2026 06:23:37 GMT
• Title: Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
• Authors: Hyun-Sik Jeong,
• Abstract summary: We show that the deep interior of the Krylov subspace maps directly to the near-horizon regime of AdSbb$$ gravity.<n>Our results advance a Krylov-based holographic dictionary in a unified $SL(2, mathR)$ representation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, $α=πT$, 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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