Krylov spread complexity as holographic complexity beyond JT gravity
Abstract
One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at infinite temperature and the complexity = volume proposal in classical JT gravity. Our work utilizes the recent connection between double-scaled SYK and sine-dilaton gravity to show that the quantitative relation between Krylov spread complexity and complexity = volume extends to finite temperatures and to full quantum regime on the gravity side at disk level. From the latter we isolate the first quantum correction to the complexity = volume proposal and propose to view it as a complexity of quantum fields in the bulk. Finally, we comment on the switchback effect, whose presence would make the Krylov spread complexity a fully fledged holographic complexity at least in sine-dilaton gravity.
Cite
@article{arxiv.2412.17785,
title = {Krylov spread complexity as holographic complexity beyond JT gravity},
author = {Michal P. Heller and Jacopo Papalini and Tim Schuhmann},
journal= {arXiv preprint arXiv:2412.17785},
year = {2025}
}
Comments
5.5 pages + supplemental, 2 figures; v2: minor improvements in the presentation, matches published version