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arXiv · 1401.8171

Torus knot polynomials and susy Wilson loops

Georgios Giasemidis·Miguel Tierz
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Abstract

We give, using an explicit expression obtained in [V. Jones, Ann. of Math. 126, 335 (1987)], a basic hypergeometric representation of the HOMFLY polynomial of $(n,m)$ torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result the $(m,n)\leftrightarrow (n,m)$ symmetry and the leading polynomial at large $N$ are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in $\mathcal{N}$=4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of $q$-harmonic oscillators.

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Georgios Giasemidis, Miguel Tierz. 2014-11-03. Torus knot polynomials and susy Wilson loops. https://doi.org/10.1007/s11005-014-0724-z

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