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

TL;DR

This paper explores non-perturbative overlaps in JT gravity to reveal universal quantum chaos signatures and introduces generating functions for quantum complexity, showing their time evolution mirrors spectral form factor behavior.

Contribution

It introduces generating functions for quantum complexity in JT gravity, linking their evolution to spectral correlators and revealing new quantum effects in black hole interiors.

Findings

Universal slope-ramp-plateau structure in complexity evolution.

Disappearance of the linear ramp as regularization decreases.

Vanishing expectation value of time shift due to quantum corrections.

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 $\langle e^{-\alpha \ell} \rangle$. 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.