Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908981678571520 |
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| author | Jeong, Hyun-Sik |
| author_facet | Jeong, Hyun-Sik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography Jeong, Hyun-Sik High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics 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. |
| title | Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2602.11627 |