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Pis'ma v Zh. Èksper. Teoret. Fiz., 2014, Volume 100, Issue 4, Pages 297–304 (Mi jetpl4105)  

This article is cited in 23 scientific papers (total in 23 papers)


Towards matrix model representation of HOMFLY polynomials

A. Aleksandrovabc, A. D. Mironovda, A. Morozova, A. A. Morozovefa

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow
b Freiburg Institute for Advanced Studies, University of Freiburg
c Mathematics Institute, University of Freiburg
d P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow
e Chelyabinsk State University
f M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We investigate possibilities of generalizing the TBEM (Tierz, Brini–Eynard–Mariño) eigenvalue matrix model, which represents the non-normalized colored HOMFLY polynomials for torus knots as averages of the corresponding characters. We look for a model of the same type, which is a usual Chern–Simons mixture of the Gaussian potential, typical for Hermitean models, and the sine Vandermonde factors, typical for the unitary ones. We mostly concentrate on the family of twist knots, which contains a single torus knot, the trefoil. It turns out that for the trefoil the TBEM measure is provided by an action of Laplace exponential on the Jones polynomial. This procedure can be applied to arbitrary knots and provides a TBEM-like integral representation for the $N=2$ case. However, beyond the torus family, both the measure and its lifting to larger $N$ contain non-trivial corrections in $\hbar=\log q$. A possibility could be to absorb these corrections into a deformation of the Laplace evolution by higher Casimir and/or cut-and-join operators, in the spirit of Hurwitz $\tau$-function approach to knot theory, but this remains a subject for future investigation.

DOI: https://doi.org/10.7868/S0370274X14160115

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English version:
Journal of Experimental and Theoretical Physics Letters, 2014, 100:4, 271–278

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Received: 16.07.2014

Citation: A. Aleksandrov, A. D. Mironov, A. Morozov, A. A. Morozov, “Towards matrix model representation of HOMFLY polynomials”, Pis'ma v Zh. Èksper. Teoret. Fiz., 100:4 (2014), 297–304; JETP Letters, 100:4 (2014), 271–278

Citation in format AMSBIB
\by A.~Aleksandrov, A.~D.~Mironov, A.~Morozov, A.~A.~Morozov
\paper Towards matrix model representation of HOMFLY polynomials
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2014
\vol 100
\issue 4
\pages 297--304
\jour JETP Letters
\yr 2014
\vol 100
\issue 4
\pages 271--278

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    4. Awata H., Kanno H., Matsumoto T., Mironov A., Morozov A., Morozov A., Ohkubo Yu., Zenkevich Y., J. High Energy Phys., 2016, no. 7, 103  crossref  mathscinet  zmath  isi  elib  scopus
    5. Morozov A., Nucl. Phys. B, 911 (2016), 582–605  crossref  zmath  isi  elib  scopus
    6. Morozov A., J. High Energy Phys., 2016, no. 9, 135  crossref  mathscinet  zmath  isi  scopus
    7. Mironov A., Morozov A., Phys. Lett. B, 755 (2016), 47–57  crossref  mathscinet  zmath  isi  elib  scopus
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    9. A. Mironov, A. Morozov, A. Morozov, P. Ramadevi, V. K. Singh, A. Sleptsov, J. Phys. A-Math. Theor., 50:8 (2017), 085201  crossref  mathscinet  zmath  isi  scopus
    10. A. Yu. Morozov, A. A. Morozov, A. V. Popolitov, Theoret. and Math. Phys., 192:1 (2017), 1039–1079  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. A. Mironov, A. Morozov, A. Morozov, P. Ramadevi, V. K. Singh, A. Sleptsov, J. High Energy Phys., 2017, no. 8, 139  crossref  mathscinet  zmath  isi  scopus
    12. A. Mironov, A. Morozov, Phys. Lett. B, 771 (2017), 503–507  crossref  zmath  isi  scopus
    13. A. Anokhina, A. Morozov, J. High Energy Phys., 2018, no. 4, 066  crossref  mathscinet  isi  scopus
    14. A. Morozov, Phys. Lett. B, 782 (2018), 104–111  crossref  mathscinet  isi  scopus
    15. A. Mironov, A. Morozov, J. High Energy Phys., 2018, no. 8, 163  crossref  isi  scopus
    16. H. Awata, H. Kanno, A. Mironov, A. Morozov, A. Morozov, Phys. Rev. D, 98:4 (2018), 046018  crossref  isi  scopus
    17. G. Borot, A. Brini, Adv. Theor. Math. Phys., 22:2 (2018), 305–394  crossref  zmath  isi  scopus
    18. A. Morozov, Phys. Lett. B, 792 (2019), 205–213  crossref  isi  scopus
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    20. A. Anokhina, A. Morozov, A. Popolitov, Eur. Phys. J. C, 79:10 (2019)  crossref  isi  scopus
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