Large-$N$ Torus Knots in Lens Spaces and Their Quiver Structure
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910070033350656 |
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| author | Bhattacharya, Ritabrata Dutta, Suvankar Pasari, Naman Verma, Nitin |
| author_facet | Bhattacharya, Ritabrata Dutta, Suvankar Pasari, Naman Verma, Nitin |
| contents | We study torus knot invariants in the lens space $S^{3}/\mathbb{Z}_{p}$ within Chern--Simons theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an $(α,β)$ torus knot in this background. In the large-$N$ limit these invariants simplify and acquire a universal form: the invariant of an $(α,β)$ torus knot in $S^{3}/\mathbb{Z}_{p}$ can be expressed in terms of the invariant of the $(α,α+pβ)$ torus knot in $S^{3}$. After an appropriate redefinition of knot variables, the generating functions of these invariants exhibit a structure analogous to quiver partition functions. Since the associated quiver is independent of the rank $N$ and level $k$ of Chern--Simons theory, the large-$N$ result provides a direct way to identify the underlying quiver, allowing us to determine the quiver structure associated with torus knots in $S^{3}/\mathbb{Z}_{p}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large-$N$ Torus Knots in Lens Spaces and Their Quiver Structure Bhattacharya, Ritabrata Dutta, Suvankar Pasari, Naman Verma, Nitin High Energy Physics - Theory Mathematical Physics We study torus knot invariants in the lens space $S^{3}/\mathbb{Z}_{p}$ within Chern--Simons theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an $(α,β)$ torus knot in this background. In the large-$N$ limit these invariants simplify and acquire a universal form: the invariant of an $(α,β)$ torus knot in $S^{3}/\mathbb{Z}_{p}$ can be expressed in terms of the invariant of the $(α,α+pβ)$ torus knot in $S^{3}$. After an appropriate redefinition of knot variables, the generating functions of these invariants exhibit a structure analogous to quiver partition functions. Since the associated quiver is independent of the rank $N$ and level $k$ of Chern--Simons theory, the large-$N$ result provides a direct way to identify the underlying quiver, allowing us to determine the quiver structure associated with torus knots in $S^{3}/\mathbb{Z}_{p}$. |
| title | Large-$N$ Torus Knots in Lens Spaces and Their Quiver Structure |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.11997 |