JT supergravity and Brezin-Gross-Witten tau-function
Abstract We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli sp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2020)160 |
| _version_ | 1818134061593395200 |
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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 thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy. |
| first_indexed | 2024-12-11T09:02:38Z |
| format | Article |
| id | doaj.art-fa37c715047644fd95fa7e8aaefc26d6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T09:02:38Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-fa37c715047644fd95fa7e8aaefc26d62022-12-22T01:13:43ZengSpringerOpenJournal of High Energy Physics1029-84792020-10-0120201013710.1007/JHEP10(2020)160JT supergravity and Brezin-Gross-Witten tau-functionKazumi Okuyama0Kazuhiro Sakai1Department of Physics, Shinshu UniversityInstitute of Physics, Meiji Gakuin UniversityAbstract We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy.http://link.springer.com/article/10.1007/JHEP10(2020)1602D GravityIntegrable HierarchiesMatrix Models |
| spellingShingle | Kazumi Okuyama Kazuhiro Sakai JT supergravity and Brezin-Gross-Witten tau-function Journal of High Energy Physics 2D Gravity Integrable Hierarchies Matrix Models |
| title | JT supergravity and Brezin-Gross-Witten tau-function |
| title_full | JT supergravity and Brezin-Gross-Witten tau-function |
| title_fullStr | JT supergravity and Brezin-Gross-Witten tau-function |
| title_full_unstemmed | JT supergravity and Brezin-Gross-Witten tau-function |
| title_short | JT supergravity and Brezin-Gross-Witten tau-function |
| title_sort | jt supergravity and brezin gross witten tau function |
| topic | 2D Gravity Integrable Hierarchies Matrix Models |
| url | http://link.springer.com/article/10.1007/JHEP10(2020)160 |
| work_keys_str_mv | AT kazumiokuyama jtsupergravityandbrezingrosswittentaufunction AT kazuhirosakai jtsupergravityandbrezingrosswittentaufunction |