On universal knot polynomials

doi:10.1007/JHEP02(2016)078

On universal knot polynomials

2016-02-12

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DOI：10.1007/JHEP02(2016)078

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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

On universal knot polynomials

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