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 random matrix theory and 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 form factor. Assuming that random matrix theory applies to chaotic CFTs, we probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random tensor component. The EFT of quantum chaos predicts that the genus-2 form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.

Belin, A., de Boer, J., Nayak, P., Sonner, J. (2022). Generalized spectral form factors and the statistics of heavy operators. JOURNAL OF HIGH ENERGY PHYSICS, 2022(11) [10.1007/JHEP11(2022)145].

Generalized spectral form factors and the statistics of heavy operators

Belin, A;
2022

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 random matrix theory and 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 form factor. Assuming that random matrix theory applies to chaotic CFTs, we probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random tensor component. The EFT of quantum chaos predicts that the genus-2 form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.
Articolo in rivista - Articolo scientifico
AdS-CFT Correspondence; Conformal Field Models in String Theory; Matrix Models;
English
25-nov-2022
2022
2022
11
145
open
Belin, A., de Boer, J., Nayak, P., Sonner, J. (2022). Generalized spectral form factors and the statistics of heavy operators. JOURNAL OF HIGH ENERGY PHYSICS, 2022(11) [10.1007/JHEP11(2022)145].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/462421
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