The ordered exponential representation of GKM using the W 1+∞ operator
Abstract The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an r-reduced tau-function that governs the r-spin intersection numbers. In this paper, we present an ordered expon...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2023)215 |
| _version_ | 1827917219619667968 |
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| author | Gehao Wang |
| author_facet | Gehao Wang |
| author_sort | Gehao Wang |
| collection | DOAJ |
| description | Abstract The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an r-reduced tau-function that governs the r-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the W 1+∞ operators that preserves the KP integrability. In fact, this representation is naturally the solution of a W 1+∞ constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their W 1+∞ representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints. |
| first_indexed | 2024-03-13T03:25:47Z |
| format | Article |
| id | doaj.art-f355ae5c062b413988fe0e7f299c9e50 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:47Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f355ae5c062b413988fe0e7f299c9e502023-06-25T11:06:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023311910.1007/JHEP03(2023)215The ordered exponential representation of GKM using the W 1+∞ operatorGehao Wang0Department of Mathematics, College of Information Science and Technology/College of Cyberspace Security, Jinan UniversityAbstract The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an r-reduced tau-function that governs the r-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the W 1+∞ operators that preserves the KP integrability. In fact, this representation is naturally the solution of a W 1+∞ constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their W 1+∞ representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints.https://doi.org/10.1007/JHEP03(2023)215Integrable HierarchiesMatrix ModelsTopological Strings |
| spellingShingle | Gehao Wang The ordered exponential representation of GKM using the W 1+∞ operator Journal of High Energy Physics Integrable Hierarchies Matrix Models Topological Strings |
| title | The ordered exponential representation of GKM using the W 1+∞ operator |
| title_full | The ordered exponential representation of GKM using the W 1+∞ operator |
| title_fullStr | The ordered exponential representation of GKM using the W 1+∞ operator |
| title_full_unstemmed | The ordered exponential representation of GKM using the W 1+∞ operator |
| title_short | The ordered exponential representation of GKM using the W 1+∞ operator |
| title_sort | ordered exponential representation of gkm using the w 1 ∞ operator |
| topic | Integrable Hierarchies Matrix Models Topological Strings |
| url | https://doi.org/10.1007/JHEP03(2023)215 |
| work_keys_str_mv | AT gehaowang theorderedexponentialrepresentationofgkmusingthew1operator AT gehaowang orderedexponentialrepresentationofgkmusingthew1operator |