Unorientable topological gravity and orthogonal random matrix universality
Abstract The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called τ−scaled limit of large times, t → ∞, and fixed temperature, in order to demonstrate agreement with universal random matrix theor...
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| Language: | English |
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2024-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2024)267 |
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| author | Torsten Weber Jarod Tall Fabian Haneder Juan Diego Urbina Klaus Richter |
| author_facet | Torsten Weber Jarod Tall Fabian Haneder Juan Diego Urbina Klaus Richter |
| author_sort | Torsten Weber |
| collection | DOAJ |
| description | Abstract The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called τ−scaled limit of large times, t → ∞, and fixed temperature, in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the unorientable Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the unorientable Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the τ−scaled SFF on the gravity side acquires both logarithmic and power law contributions in t, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity. |
| format | Article |
| id | doaj-art-71756cad77eb41bfabca0216dac770f1 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-71756cad77eb41bfabca0216dac770f12024-12-08T12:07:51ZengSpringerOpenJournal of High Energy Physics1029-84792024-07-012024714910.1007/JHEP07(2024)267Unorientable topological gravity and orthogonal random matrix universalityTorsten Weber0Jarod Tall1Fabian Haneder2Juan Diego Urbina3Klaus Richter4Institut für Theoretische Physik, Universität RegensburgDepartment of Physics and Astronomy, Washington State UniversityInstitut für Theoretische Physik, Universität RegensburgInstitut für Theoretische Physik, Universität RegensburgInstitut für Theoretische Physik, Universität RegensburgAbstract The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called τ−scaled limit of large times, t → ∞, and fixed temperature, in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the unorientable Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the unorientable Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the τ−scaled SFF on the gravity side acquires both logarithmic and power law contributions in t, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity.https://doi.org/10.1007/JHEP07(2024)2672D GravityMatrix ModelsAdS-CFT Correspondence |
| spellingShingle | Torsten Weber Jarod Tall Fabian Haneder Juan Diego Urbina Klaus Richter Unorientable topological gravity and orthogonal random matrix universality Journal of High Energy Physics 2D Gravity Matrix Models AdS-CFT Correspondence |
| title | Unorientable topological gravity and orthogonal random matrix universality |
| title_full | Unorientable topological gravity and orthogonal random matrix universality |
| title_fullStr | Unorientable topological gravity and orthogonal random matrix universality |
| title_full_unstemmed | Unorientable topological gravity and orthogonal random matrix universality |
| title_short | Unorientable topological gravity and orthogonal random matrix universality |
| title_sort | unorientable topological gravity and orthogonal random matrix universality |
| topic | 2D Gravity Matrix Models AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP07(2024)267 |
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