Krylov spread complexity as holographic complexity beyond JT gravity

TL;DR

This paper establishes a quantitative link between Krylov spread complexity in SYK models and holographic complexity in sine-dilaton gravity, extending previous results to finite temperatures and quantum regimes, and identifying quantum corrections.

Contribution

It demonstrates that the relation between Krylov spread complexity and holographic complexity extends beyond JT gravity to sine-dilaton gravity at finite temperatures and quantum levels, including quantum corrections.

Findings

Krylov spread complexity matches complexity=volume in sine-dilaton gravity.

Quantum corrections to holographic complexity are identified.

The relation holds at finite temperature and quantum regimes.

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.