Non-perturbative Overlaps in JT Gravity: From Spectral Form Factor to Generating Functions of Complexity

Abstract

The interplay between black hole interior dynamics and quantum chaos provides a crucial framework for probing quantum effects in quantum gravity. In this work, we investigate non-perturbative overlaps in Jackiw-Teitelboim (JT) gravity to uncover universal signatures of quantum chaos and quantum complexity. Taking advantage of universal spectral correlators from random matrix theory, we compute the overlaps between the thermofield double (TFD) state and two distinct classes of states: fixed-length states, which encode maximal volume slices, and time-shifted TFD states. The squared overlaps naturally define probability distributions that quantify the expectation values of gravitational observables. Central to our results is the introduction of generating functions for quantum complexity measures, such as $⟨e^{-\alpha \ell }⟩$. The time evolution of these generating functions exhibits the universal slope-ramp-plateau structure, mirroring the behavior of the spectral form factor (SFF). Using generating functions, we further demonstrate that the universal time evolution of complexity for chaotic systems, which is characterized by a linear growth followed by a late-time plateau, arises from the disappearance of the linear ramp as the regularization parameter $\alpha$ decreases. With regard to the time-shifted TFD state, we derive a surprising result: the expectation value of the time shift, which classically grows linearly, vanishes when non-perturbative quantum corrections are incorporated. This cancellation highlights a fundamental distinction between semiclassical and quantum gravitational descriptions of the black hole interior. All our findings establish generating functions as powerful probes of quantum complexity and chaos in gravitational and quantum systems.

68 pages, many figures; v2: references added; v3: corrected typos, added a new plot, published version

References in corpus (44)

• Comments on the Sachdev-Ye-Kitaev model
• Eternal Black Holes in AdS
• Black Holes: Complementarity or Firewalls?
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• An Investigation of AdS${}_2$ Backreaction and Holography
• Complexity, action, and black holes
• Quantum Computation as Geometry
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Wormholes in AdS
• An Apologia for Firewalls
• The Second Law of Quantum Complexity
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Quantum chaos and the complexity of spread of states
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• On geodesic propagators and black hole holography
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• Gravity Dual of Quantum Information Metric
• Quantum Complexity and Negative Curvature
• Linear growth of quantum circuit complexity
• Gravity/Ensemble Duality
• The bulk Hilbert space of double scaled SYK
• Does Complexity Equal Anything?
• Eigenstate Thermalization and Disorder Averaging in Gravity
• Universal chaotic dynamics from Krylov space
• Observations of Hawking radiation: the Page curve and baby universes
• Complexity growth of operators in the SYK model and in JT gravity
• The Typical-State Paradox: Diagnosing Horizons with Complexity
• Complexity and the bulk volume, a new York time story
• Thermalization of the spectral function in strongly coupled two dimensional conformal field theories
• Unitarity From a Smooth Horizon?
• Evolution of Two-Point Functions from Holography
• Complexity Equals Anything II
• Krylov complexity of density matrix operators
• Gravity factorized
• Spectral and Krylov Complexity in Billiard Systems
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• An integrable road to a perturbative plateau
• Ensemble from Coarse Graining: Reconstructing the Interior of an Evaporating Black Hole
• Krylov complexity as an order parameter for quantum chaotic-integrable transitions
• Complexity=Anything: Singularity Probes
• Butterflies from Information Metric
• Spectral form factor in the $\tau$-scaling limit

Cited by in corpus (4)

• Toward Krylov-based holography in double-scaled SYK
• The landscape of complexity measures in 2D gravity
• Universal Time Evolution of Holographic and Quantum Complexity
• York time in JT gravity