Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n
In this work we study the tau-function Z1D of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces M‾g,n of stable curves. The first is to use (fat or thin) topological recur...
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| Format: | Article |
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Elsevier
2025-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032132500032X |
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| author | Zhiyuan Wang Jian Zhou |
| author_facet | Zhiyuan Wang Jian Zhou |
| author_sort | Zhiyuan Wang |
| collection | DOAJ |
| description | In this work we study the tau-function Z1D of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces M‾g,n of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for Z1D; and the second is to use a formula for the connected n-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work [34]. |
| format | Article |
| id | doaj-art-63f02567802a415eaaf043fc051b4318 |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-63f02567802a415eaaf043fc051b43182025-02-09T04:59:42ZengElsevierNuclear Physics B0550-32132025-03-011012116822Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,nZhiyuan Wang0Jian Zhou1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; Corresponding author.Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, ChinaIn this work we study the tau-function Z1D of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of the moduli spaces M‾g,n of stable curves. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for Z1D; and the second is to use a formula for the connected n-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work [34].http://www.sciencedirect.com/science/article/pii/S055032132500032X |
| spellingShingle | Zhiyuan Wang Jian Zhou Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n Nuclear Physics B |
| title | Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n |
| title_full | Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n |
| title_fullStr | Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n |
| title_full_unstemmed | Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n |
| title_short | Topological 1D gravity, KP hierarchy, and orbifold Euler characteristics of M‾g,n |
| title_sort | topological 1d gravity kp hierarchy and orbifold euler characteristics of m‾g n |
| url | http://www.sciencedirect.com/science/article/pii/S055032132500032X |
| work_keys_str_mv | AT zhiyuanwang topological1dgravitykphierarchyandorbifoldeulercharacteristicsofmgn AT jianzhou topological1dgravitykphierarchyandorbifoldeulercharacteristicsofmgn |