Toward Krylov-based holography in double-scaled SYK
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| Format: | Preprint |
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2025
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| _version_ | 1866911684879187968 |
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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 |