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Journal of High Energy Physics

, 2016:78 | Cite as

On universal knot polynomials

  • A. Mironov
  • R. Mkrtchyan
  • A. Morozov
Open Access
Regular Article - Theoretical Physics

Abstract

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel’s plane, respectively and give their exceptional group’s counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel’s plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Keywords

Quantum Groups Chern-Simons Theories Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Lebedev Physics InstituteMoscowRussia
  2. 2.ITEPMoscowRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia
  4. 4.National Research Nuclear University MEPhIMoscowRussia
  5. 5.Yerevan Physics InstituteYerevanArmenia

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