Recursion relations and BPS-expansions in the HOMFLY-PT skein of the solid torus
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918299818786816 |
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| author | Nakamura, Lukas |
| author_facet | Nakamura, Lukas |
| contents | Inspired by the skein valued open Gromov-Witten theory of Ekholm and Shende and the Gopakumar-Vafa formula, we associate to each pair of non-negative integers $(g,l)$ a formal power series with values in the HOMFLY-PT skein of a disjoint union of $l$ solid tori. The formal power series can be thought of as open BPS-states of genus $g$ with $l$ boundary components and reduces to the contribution of a single BPS state of genus $g$ for $l=0$. Using skein theoretic methods we show that the formal power series satisfy gluing identities and multi-cover skein relations corresponding to an elliptic boundary node of the underlying curves. For $(g,l)=(0,1)$ we prove a crossing formula which is the multi-cover skein relation corresponding to a hyperbolic boundary node, also known as the pentagon identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursion relations and BPS-expansions in the HOMFLY-PT skein of the solid torus Nakamura, Lukas Quantum Algebra Symplectic Geometry Inspired by the skein valued open Gromov-Witten theory of Ekholm and Shende and the Gopakumar-Vafa formula, we associate to each pair of non-negative integers $(g,l)$ a formal power series with values in the HOMFLY-PT skein of a disjoint union of $l$ solid tori. The formal power series can be thought of as open BPS-states of genus $g$ with $l$ boundary components and reduces to the contribution of a single BPS state of genus $g$ for $l=0$. Using skein theoretic methods we show that the formal power series satisfy gluing identities and multi-cover skein relations corresponding to an elliptic boundary node of the underlying curves. For $(g,l)=(0,1)$ we prove a crossing formula which is the multi-cover skein relation corresponding to a hyperbolic boundary node, also known as the pentagon identity. |
| title | Recursion relations and BPS-expansions in the HOMFLY-PT skein of the solid torus |
| topic | Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2401.10730 |