Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos
Abstract We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete pa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2023)161 |
| _version_ | 1827301429671362560 |
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| author | Felix M. Haehl Wyatt Reeves Moshe Rozali |
| author_facet | Felix M. Haehl Wyatt Reeves Moshe Rozali |
| author_sort | Felix M. Haehl |
| collection | DOAJ |
| description | Abstract We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity. |
| first_indexed | 2024-03-08T18:17:12Z |
| format | Article |
| id | doaj.art-fdce062bf3a64e2199e71892e0d50df1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T16:22:59Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-fdce062bf3a64e2199e71892e0d50df12024-03-31T11:07:15ZengSpringerOpenJournal of High Energy Physics1029-84792023-12-0120231214810.1007/JHEP12(2023)161Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaosFelix M. Haehl0Wyatt Reeves1Moshe Rozali2School of Mathematical Sciences and STAG Research Centre, University of SouthamptonDepartment of Physics and Astronomy, University of British ColumbiaDepartment of Physics and Astronomy, University of British ColumbiaAbstract We continue the study of random matrix universality in two-dimensional conformal field theories. This is facilitated by expanding the spectral form factor in a basis of modular invariant eigenfunctions of the Laplacian on the fundamental domain. The focus of this paper is on the discrete part of the spectrum, which consists of the Maass cusp forms. Both their eigenvalues and Fourier coefficients are sporadic discrete numbers with interesting statistical properties and relations to analytic number theory; this is referred to as ‘arithmetic chaos’. We show that the near-extremal spectral form factor at late times is only sensitive to a statistical average over these erratic features. Nevertheless, complete information about their statistical distributions is encoded in the spectral form factor if all its spin sectors exhibit universal random matrix eigenvalue repulsion (a ‘linear ramp’). We ‘bootstrap’ the spectral correlations between the cusp form basis functions that correspond to a universal linear ramp and show that they are unique up to theory-dependent subleading corrections. The statistical treatment of cusp forms provides a natural avenue to fix the subleading corrections in a minimal way, which we observe leads to the same correlations as those described by the [torus]×[interval] wormhole amplitude in AdS3 gravity.https://doi.org/10.1007/JHEP12(2023)161AdS-CFT CorrespondenceConformal and W SymmetryRandom Systems |
| spellingShingle | Felix M. Haehl Wyatt Reeves Moshe Rozali Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Random Systems |
| title | Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos |
| title_full | Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos |
| title_fullStr | Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos |
| title_full_unstemmed | Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos |
| title_short | Symmetries and spectral statistics in chaotic conformal field theories. Part II. Maass cusp forms and arithmetic chaos |
| title_sort | symmetries and spectral statistics in chaotic conformal field theories part ii maass cusp forms and arithmetic chaos |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Random Systems |
| url | https://doi.org/10.1007/JHEP12(2023)161 |
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