$U(N)$ Torus Link Invariants in the Large $N$ limit from Matrix Model Approach
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913268202733568 |
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| author | Maji, Archana Chakraborty, Kushal Dutta, Suvankar Ramadevi, P. |
| author_facet | Maji, Archana Chakraborty, Kushal Dutta, Suvankar Ramadevi, P. |
| contents | In this paper we study $U(N)$ colored HOMFLY-PT polynomials of torus links in the double scaling limit (polynomial variable $q\rightarrow 1$, $N\rightarrow \infty$ keeping $q^N$ fixed). We show that, in this limit, the colored HOMFLY-PT polynomial of any $(Lα,Lβ)$ torus link can be expressed in terms of the colored HOMFLY-PT polynomial of $(L,L)$ torus link. Using the connection between matrix models and the Chern-Simons field theoretic invariants, we show that the colored torus link invariants are uniquely expressed in terms of connected correlation functions of operators in $U(N)$ matrix model. We determine the leading and subleading contribution to some of the correlators at large $N$ from the matrix model approach and find that they match exactly with those obtained from the corresponding colored HOMFLY-PT polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14113 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $U(N)$ Torus Link Invariants in the Large $N$ limit from Matrix Model Approach Maji, Archana Chakraborty, Kushal Dutta, Suvankar Ramadevi, P. High Energy Physics - Theory In this paper we study $U(N)$ colored HOMFLY-PT polynomials of torus links in the double scaling limit (polynomial variable $q\rightarrow 1$, $N\rightarrow \infty$ keeping $q^N$ fixed). We show that, in this limit, the colored HOMFLY-PT polynomial of any $(Lα,Lβ)$ torus link can be expressed in terms of the colored HOMFLY-PT polynomial of $(L,L)$ torus link. Using the connection between matrix models and the Chern-Simons field theoretic invariants, we show that the colored torus link invariants are uniquely expressed in terms of connected correlation functions of operators in $U(N)$ matrix model. We determine the leading and subleading contribution to some of the correlators at large $N$ from the matrix model approach and find that they match exactly with those obtained from the corresponding colored HOMFLY-PT polynomials. |
| title | $U(N)$ Torus Link Invariants in the Large $N$ limit from Matrix Model Approach |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.14113 |