Knot contact homology as a planar limit of Chern-Simons theory
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912901986516992 |
|---|---|
| author | Webster, Ben Zaimi, Meri |
| author_facet | Webster, Ben Zaimi, Meri |
| contents | We prove a conjecture relating augmentation varieties to the large $N$ limit of Chern-Simons theory. Although this does not directly establish that the augmentation polynomial of a knot is the classical limit of a deformed $\hat{A}$-polynomial -- as suggested by Aganagić and Vafa -- it reduces the problem to characterizing certain algebraic properties of a module over the quantum torus, introduced in work of Gaiotto, Kannagi, and Sanjurjo. We term this the \emph{HOMFLYPT difference module}, which captures relations between the colored HOMFLYPT polynomials of different antisymmetric colorings. We demonstrate that the classical limit of this difference module for a knot is precisely the degree 0 abelianized knot contact homology of the knot, and we provide a natural extension of this result to links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12404 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Knot contact homology as a planar limit of Chern-Simons theory Webster, Ben Zaimi, Meri Geometric Topology Quantum Algebra Representation Theory We prove a conjecture relating augmentation varieties to the large $N$ limit of Chern-Simons theory. Although this does not directly establish that the augmentation polynomial of a knot is the classical limit of a deformed $\hat{A}$-polynomial -- as suggested by Aganagić and Vafa -- it reduces the problem to characterizing certain algebraic properties of a module over the quantum torus, introduced in work of Gaiotto, Kannagi, and Sanjurjo. We term this the \emph{HOMFLYPT difference module}, which captures relations between the colored HOMFLYPT polynomials of different antisymmetric colorings. We demonstrate that the classical limit of this difference module for a knot is precisely the degree 0 abelianized knot contact homology of the knot, and we provide a natural extension of this result to links. |
| title | Knot contact homology as a planar limit of Chern-Simons theory |
| topic | Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2602.12404 |