Abstract
We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin (“spectral determinacy”). We then describe an argument analogous to the one leading to Cardy’s formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.
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Acknowledgments
We thank Eric Perlmutter for comments on a draft and Scott Collier for very helpful comments on the role of Maass cusp forms. We further thank Jonah Berean-Dutcher, Kristan Jensen, Henry Maxfield, Chistopher Waddell, David Wakeham for useful conversation. FH is supported by the UKRI Frontier Research Grant EP/X030334/1 and acknowledges support by the DOE grant DE-SC0009988 during the early stages of this project. CM, WR and MR are supported by a Discovery grant from NSERC.
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Haehl, F.M., Marteau, C., Reeves, W. et al. Symmetries and spectral statistics in chaotic conformal field theories. J. High Energ. Phys. 2023, 196 (2023). https://doi.org/10.1007/JHEP07(2023)196
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DOI: https://doi.org/10.1007/JHEP07(2023)196