Hopf link invariants and integrable hierarchies
The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269324007287 |
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| author | Chuanzhong Li A. Mironov A.Yu. Orlov |
| author_facet | Chuanzhong Li A. Mironov A.Yu. Orlov |
| author_sort | Chuanzhong Li |
| collection | DOAJ |
| description | The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a τ-function of the universal character (UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy. |
| format | Article |
| id | doaj-art-b8ccb28c4c9a4b7291b36dd77ffd3ad2 |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-b8ccb28c4c9a4b7291b36dd77ffd3ad22025-01-10T04:37:22ZengElsevierPhysics Letters B0370-26932025-01-01860139170Hopf link invariants and integrable hierarchiesChuanzhong Li0A. Mironov1A.Yu. Orlov2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, ChinaLebedev Physics Institute, Moscow 119991, Russia; ITEP, Moscow 117218, Russia; Institute for Information Transmission Problems, Moscow 127994, Russia; Corresponding author.Shirshov Institute of Oceanology, RAS, Nahimovskii Prospekt 36, Moscow 117997, RussiaThe goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a τ-function of the universal character (UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy.http://www.sciencedirect.com/science/article/pii/S0370269324007287 |
| spellingShingle | Chuanzhong Li A. Mironov A.Yu. Orlov Hopf link invariants and integrable hierarchies Physics Letters B |
| title | Hopf link invariants and integrable hierarchies |
| title_full | Hopf link invariants and integrable hierarchies |
| title_fullStr | Hopf link invariants and integrable hierarchies |
| title_full_unstemmed | Hopf link invariants and integrable hierarchies |
| title_short | Hopf link invariants and integrable hierarchies |
| title_sort | hopf link invariants and integrable hierarchies |
| url | http://www.sciencedirect.com/science/article/pii/S0370269324007287 |
| work_keys_str_mv | AT chuanzhongli hopflinkinvariantsandintegrablehierarchies AT amironov hopflinkinvariantsandintegrablehierarchies AT ayuorlov hopflinkinvariantsandintegrablehierarchies |