Krylov Spread Complexity as Holographic Complexity beyond Jackiw-Teitelboim Gravity.

Area of Science:

• Quantum Gravity
• Quantum Information Theory
• Black Hole Physics

Background:

• Holographic complexity proposals lack dual interpretations, with only the Sachdev-Ye-Kitaev (SYK) model showing a quantitative match to the complexity = volume (CV) proposal.
• The CV proposal relates gravitational complexity to the volume of a spatial slice in the black hole interior.

Purpose of the Study:

• To extend the quantitative match between Krylov spread complexity and the CV proposal to finite temperatures and the full quantum regime.
• To investigate quantum corrections to the CV proposal and their interpretation in the context of quantum field theory in the bulk.

Main Methods:

• Utilizing the connection between the double-scaled SYK model and sine dilaton gravity.
• Analyzing the Krylov spread complexity in the SYK model at finite temperatures.
• Calculating quantum corrections to the CV proposal in Jackiw-Teitelboim gravity.

Main Results:

• The quantitative relation between Krylov spread complexity and CV proposal holds at finite temperatures and in the full quantum regime at disk level.
• The first quantum correction to the CV proposal was isolated and interpreted as the complexity of quantum fields in the bulk.
• A key finding is that gravity necessitates assigning complexity to Euclidean state preparation.

Conclusions:

• The study establishes a robust connection between quantum information-theoretic complexity and holographic gravity, extending previous findings.
• Quantum corrections provide new insights into the nature of complexity in quantum gravity.
• The results suggest a deeper understanding of quantum black holes and the holographic principle is achievable through these complexity measures.