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hep-thDec 1, 2025
authors
  • Andrei Mironov
  • Vivek Kumar Singh
institutions
  • Institute for Information Transmission Problems
  • Kurchatov Institute
  • New York University
  • P.N. Lebedev Physical Institute of the Russian Academy of Sciences
arXiv abstractPDF
paper

Torus Knots in Adjoint Representation

arXiv:2512.23095 · doi:10.1103/ncsr-z788

Abstract

We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.

typos corrected, refs updated

References in corpus (13)

  • Chern-Simons Theory and Topological Strings
  • On the Hecke algebras and the colored HOMFLY polynomial
  • Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
  • On universal knot polynomials
  • Universality in Chern-Simons theory
  • Nonperturbative universal Chern-Simons theory
  • Equations on knot polynomials and 3d/5d duality
  • Cabling procedure for the colored HOMFLY polynomials
  • On Hopf-induced deformation of topological locus
  • Partition function of Chern-Simons theory as renormalized q-dimension
  • Macdonald deformation of Vogel's universality and link hyperpolynomials
  • Can Yang-Baxter imply Lie algebra?
  • Torus knots in adjoint representation and Vogel's universality
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