Journal
COMMUNICATIONS IN NUMBER THEORY AND PHYSICS
Volume 13, Issue 4, Pages 763-826Publisher
INT PRESS BOSTON, INC
DOI: 10.4310/CNTP.2019.v13.n4.a3
Keywords
HOMFLY-PT polynomials; torus knots; free fermions; Ooguri-Vafa partition function; spectral curve; Chekhov-Eynard-Orantin topological recursion; Hurwitz numbers; Jacobi polynomials
Categories
Funding
- Netherlands Organization for Scientific Research
- Russian Science Foundation [16-12-10344]
- RFBR [16-31-60044-mol a dk, 18-01-00461, 18-31-20046-mol a ved]
- Russian Academic Excellence Project '5-100'
- Russian Science Foundation [19-12-13040] Funding Source: Russian Science Foundation
Ask authors/readers for more resources
We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This allows us to conjecture the combinatorial meaning of full expansion of the correlation differentials obtained via the topological recursion on the Brini-Eynard-Marino spectral curve for the colored HOMFLY-PT polynomials of torus knots. This correspondence suggests a structural combinatorial result for the extended Ooguri-Vafa partition function. Namely, its coefficients should have a quasi-polynomial behavior, where non-polynomial factors are given by the Jacobi polynomials (treated as functions of their parameters in which they are indeed non-polynomial). We prove this quasi-polynomiality in a purely combinatorial way. In addition to that, we show that the (0,1)- and (0,2)-functions on the corresponding spectral curve are in agreement with the extension of the colored HOMFLY-PT polynomials data, and we prove the quantum spectral curve equation for a natural wave function obtained from the extended Ooguri-Vafa partition function.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available