JT gravity, KdV equations and macroscopic loop operators
Abstract We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 background using the matrix model description recently found by Saad, Shenker and Stanford [ arXiv:1903.11115 ]. We show that the partition function of JT gravity is written as the exp...
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)156 |
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| author | Kazumi Okuyama Kazuhiro Sakai |
| author_facet | Kazumi Okuyama Kazuhiro Sakai |
| author_sort | Kazumi Okuyama |
| collection | DOAJ |
| description | Abstract We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 background using the matrix model description recently found by Saad, Shenker and Stanford [ arXiv:1903.11115 ]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit. |
| format | Article |
| id | doaj-art-2a1bafe5b1fc4db4be5c99ef548884eb |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2a1bafe5b1fc4db4be5c99ef548884eb2025-01-26T12:11:33ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114510.1007/JHEP01(2020)156JT gravity, KdV equations and macroscopic loop operatorsKazumi Okuyama0Kazuhiro Sakai1Department of Physics, Shinshu UniversityInstitute of Physics, Meiji Gakuin UniversityAbstract We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS2 background using the matrix model description recently found by Saad, Shenker and Stanford [ arXiv:1903.11115 ]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.https://doi.org/10.1007/JHEP01(2020)1562D GravityMatrix ModelsIntegrable Hierarchies |
| spellingShingle | Kazumi Okuyama Kazuhiro Sakai JT gravity, KdV equations and macroscopic loop operators Journal of High Energy Physics 2D Gravity Matrix Models Integrable Hierarchies |
| title | JT gravity, KdV equations and macroscopic loop operators |
| title_full | JT gravity, KdV equations and macroscopic loop operators |
| title_fullStr | JT gravity, KdV equations and macroscopic loop operators |
| title_full_unstemmed | JT gravity, KdV equations and macroscopic loop operators |
| title_short | JT gravity, KdV equations and macroscopic loop operators |
| title_sort | jt gravity kdv equations and macroscopic loop operators |
| topic | 2D Gravity Matrix Models Integrable Hierarchies |
| url | https://doi.org/10.1007/JHEP01(2020)156 |
| work_keys_str_mv | AT kazumiokuyama jtgravitykdvequationsandmacroscopicloopoperators AT kazuhirosakai jtgravitykdvequationsandmacroscopicloopoperators |