Generalized Spectral Form Factors and the Statistics of Heavy Operators
arXiv:2111.06373 · doi:10.1007/JHEP11(2022)145
Abstract
The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories. In this paper, we introduce generalized spectral form factors: new probes of quantum chaos sensitive to the dynamical data of a theory. These quantities can be studied using an effective theory of quantum chaos. We focus our attention on a particular combination of heavy-heavy-heavy OPE coefficients that generalizes the genus-2 partition function of two-dimensional CFTs, for which we define a spectral form factor. We probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random matrix component in the ergodic regime. The EFT of quantum chaos predicts that the genus-2 spectral form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.
arXiv comment35 pages, 3 figures; v2 minor comments added, clarification on the statistics of OPE coefficients
References in corpus (40)
- Chaos and Quantum Thermalization
- Random-Matrix Theory of Quantum Transport
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Eternal Black Holes in AdS
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Wormholes in AdS
- Virasoro Conformal Blocks and Thermality from Classical Background Fields
- OPE Convergence in Conformal Field Theory
- Random Statistics of OPE Coefficients and Euclidean Wormholes
- AdS gravity and random CFT
- Eigenstate Thermalization and Disorder Averaging in Gravity
- Eigenstate thermalization in the Sachdev-Ye-Kitaev model
- Universal Dynamics of Heavy Operators in CFT
- Quantum ergodicity in the SYK model
- A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Late time physics of holographic quantum chaos
- Disordered Quivers and Cold Horizons
- Probing thermality beyond the diagonal
- ETH and Modular Invariance of 2D CFTs
- Analytic Euclidean Bootstrap
- On thermality of CFT eigenstates
- Gravitational Constrained Instantons
- Heavy Operators and Hydrodynamic Tails
- A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
- Typicality and thermality in 2d CFT
- Bound on Eigenstate Thermalization from Transport
- Generalized Eigenstate Thermalization in 2d CFTs
- Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
- Modular crossings, OPE coefficients and black holes
- OPE statistics from higher-point crossing
- From operator statistics to wormholes
- Genus Two Partition Functions and Renyi Entropies of Large c CFTs
- Quantum thermalization and Virasoro symmetry
- Note on ETH of descendant states in 2D CFT
- The Most Irrational Rational Theories
- Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
- Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
- Statistical coupling constants from hidden sector entanglement
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- Semiclassical 3D gravity as an average of large-c CFTs
- Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
- Universal Asymptotics for High Energy CFT Data
- An integrable road to a perturbative plateau
- Wormholes from heavy operator statistics in AdS/CFT
- A principle of maximum ignorance for semiclassical gravity
- Multiboundary wormholes and OPE statistics
- Symmetries and spectral statistics in chaotic conformal field theories
- Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
- Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces
- Factorization and global symmetries in holography
- A Reverse Black Hole Information Problem
- A universal sum over topologies in 3d gravity