Toward Krylov-based holography in double-scaled SYK

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Main Authors: Fu, Yichao, Jeong, Hyun-Sik, Kim, Keun-Young, Pedraza, Juan F.
Format: Preprint
Published: 2025
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author Fu, Yichao
Jeong, Hyun-Sik
Kim, Keun-Young
Pedraza, Juan F.
author_facet Fu, Yichao
Jeong, Hyun-Sik
Kim, Keun-Young
Pedraza, Juan F.
contents Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK). First, we demonstrate that the growth rate of Krylov state complexity corresponds to the wormhole velocity, and show that its expectation value in coherent states serves as a boundary diagnostic of firewall-like structures via bulk reconstruction. We also delineate an alternative bulk description in terms of the proper momentum of an infalling particle at early times, establishing a threefold duality between the Krylov complexity growth rate, wormhole velocity, and proper momentum, with clear regimes of validity. Beyond the first moments, we argue that higher-order Krylov complexities capture connected bulk contributions encoded by replica wormholes, while the logarithmic variant probes the replica saddle structure. Finally, within a third-quantized setting incorporating baby universes, we show that the Krylov entropy equals the von Neumann entropy of the parent-geometry density matrix obtained after tracing out baby universes, thereby quantifying information flow into the baby universe sector. Together, these results elevate Krylov-space observables to sharp probes of bulk dynamics and topology in ensemble-averaged 2D gravity.
format Preprint
id arxiv_https___arxiv_org_abs_2510_22658
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Toward Krylov-based holography in double-scaled SYK
Fu, Yichao
Jeong, Hyun-Sik
Kim, Keun-Young
Pedraza, Juan F.
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev model (DSSYK). First, we demonstrate that the growth rate of Krylov state complexity corresponds to the wormhole velocity, and show that its expectation value in coherent states serves as a boundary diagnostic of firewall-like structures via bulk reconstruction. We also delineate an alternative bulk description in terms of the proper momentum of an infalling particle at early times, establishing a threefold duality between the Krylov complexity growth rate, wormhole velocity, and proper momentum, with clear regimes of validity. Beyond the first moments, we argue that higher-order Krylov complexities capture connected bulk contributions encoded by replica wormholes, while the logarithmic variant probes the replica saddle structure. Finally, within a third-quantized setting incorporating baby universes, we show that the Krylov entropy equals the von Neumann entropy of the parent-geometry density matrix obtained after tracing out baby universes, thereby quantifying information flow into the baby universe sector. Together, these results elevate Krylov-space observables to sharp probes of bulk dynamics and topology in ensemble-averaged 2D gravity.
title Toward Krylov-based holography in double-scaled SYK
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
url https://arxiv.org/abs/2510.22658