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Generalized Spectral Form Factors and the Statistics of Heavy Operators
- Source :
- JHEP 11 (2022) 145
- Publication Year :
- 2021
-
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.<br />Comment: 35 pages, 3 figures; v2 minor comments added, clarification on the statistics of OPE coefficients
- Subjects :
- High Energy Physics - Theory
Condensed Matter - Strongly Correlated Electrons
Subjects
Details
- Database :
- arXiv
- Journal :
- JHEP 11 (2022) 145
- Publication Type :
- Report
- Accession number :
- edsarx.2111.06373
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP11(2022)145