A proof of loop equations in 2d topological gravity
Abstract We study multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the presence of general couplings t k . We clarify all t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2021)107 |
| _version_ | 1819021968761946112 |
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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 multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the presence of general couplings t k . We clarify all the details, in particular the treatment of the genus zero part of the one-boundary correlator. The loop equations are verified by several new examples, including the correlators of Jackiw-Teitelboim gravity in the genus expansion and the exact correlators in the Airy case. We also discuss the free boson/fermion representation of the correlators and compare it with the formulation of Marolf and Maxfield and the string field theory of Ishibashi and Kawai. We find similarities but also some differences. |
| first_indexed | 2024-12-21T04:15:32Z |
| format | Article |
| id | doaj.art-94dfeb2b2b304a8ba35dd355e944d976 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T04:15:32Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-94dfeb2b2b304a8ba35dd355e944d9762022-12-21T19:16:19ZengSpringerOpenJournal of High Energy Physics1029-84792021-10-0120211013210.1007/JHEP10(2021)107A proof of loop equations in 2d topological gravityKazumi Okuyama0Kazuhiro Sakai1Department of Physics, Shinshu UniversityInstitute of Physics, Meiji Gakuin UniversityAbstract We study multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the presence of general couplings t k . We clarify all the details, in particular the treatment of the genus zero part of the one-boundary correlator. The loop equations are verified by several new examples, including the correlators of Jackiw-Teitelboim gravity in the genus expansion and the exact correlators in the Airy case. We also discuss the free boson/fermion representation of the correlators and compare it with the formulation of Marolf and Maxfield and the string field theory of Ishibashi and Kawai. We find similarities but also some differences.https://doi.org/10.1007/JHEP10(2021)1072D GravityMatrix ModelsIntegrable Hierarchies |
| spellingShingle | Kazumi Okuyama Kazuhiro Sakai A proof of loop equations in 2d topological gravity Journal of High Energy Physics 2D Gravity Matrix Models Integrable Hierarchies |
| title | A proof of loop equations in 2d topological gravity |
| title_full | A proof of loop equations in 2d topological gravity |
| title_fullStr | A proof of loop equations in 2d topological gravity |
| title_full_unstemmed | A proof of loop equations in 2d topological gravity |
| title_short | A proof of loop equations in 2d topological gravity |
| title_sort | proof of loop equations in 2d topological gravity |
| topic | 2D Gravity Matrix Models Integrable Hierarchies |
| url | https://doi.org/10.1007/JHEP10(2021)107 |
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