Non-perturbative effects in JT gravity from KdV equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910961878695936 |
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| author | Hatsuda, Yasuyuki Matsumoto, Takaki Okuyama, Kazumi |
| author_facet | Hatsuda, Yasuyuki Matsumoto, Takaki Okuyama, Kazumi |
| contents | It is well-known that the partition function of the Jackiw-Teitelboim (JT) gravity is obtained by an integral transformation of volumes of moduli spaces for Riemann surfaces, also known as the Weil-Petersson volumes. This fact enables us to compute the perturbative genus expansion of the partition function by solving a KdV-type non-linear partial differential equation. In this work, we find that this KdV equation also admits transseries solutions. We give a systematic algorithm to explicitly construct a one-parameter transseries solution to the KdV equation. Our approach is based on general two-dimensional topological gravity, and the results for the JT gravity are easily obtained as a special case. The results in the leading non-perturbative sector perfectly agree with another independent calculation from topological recursions in random matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-perturbative effects in JT gravity from KdV equations Hatsuda, Yasuyuki Matsumoto, Takaki Okuyama, Kazumi High Energy Physics - Theory Mathematical Physics It is well-known that the partition function of the Jackiw-Teitelboim (JT) gravity is obtained by an integral transformation of volumes of moduli spaces for Riemann surfaces, also known as the Weil-Petersson volumes. This fact enables us to compute the perturbative genus expansion of the partition function by solving a KdV-type non-linear partial differential equation. In this work, we find that this KdV equation also admits transseries solutions. We give a systematic algorithm to explicitly construct a one-parameter transseries solution to the KdV equation. Our approach is based on general two-dimensional topological gravity, and the results for the JT gravity are easily obtained as a special case. The results in the leading non-perturbative sector perfectly agree with another independent calculation from topological recursions in random matrices. |
| title | Non-perturbative effects in JT gravity from KdV equations |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.16433 |