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• W3099719910 abstract "Using the correspondence between Chern-Simons theories and Wess-Zumino-Witten models, we present the necessary tools to calculate colored HOMFLY polynomials for hyperbolic knots. For two-bridge hyperbolic knots we derive the colored HOMFLY invariants in terms of crossing matrices of the underlying Wess-Zumino-Witten model. Our analysis extends previous works by incorporating non-trivial multiplicities for the primaries appearing in the crossing matrices, so as to describe colorings of HOMFLY invariants beyond the totally symmetric or anti-symmetric representations of SU(N). The crossing matrices directly relate to 6j-symbols of the quantum group $${mathcal{U}_{q}su(N)}$$ . We present powerful methods to calculate such quantum 6j-symbols for general N. This allows us to determine previously unknown colored HOMFLY polynomials for two-bridge hyperbolic knots. We give explicitly the HOMFLY polynomials colored by the representation {2, 1} for two-bridge hyperbolic knots with up to eight crossings. Yet, the scope of application of our techniques goes beyond knot theory; e.g., our findings can be used to study correlators in Wess-Zumino-Witten conformal field theories or—in the limit to classical groups—to determine color factors for Yang Mills amplitudes." @default.
• W3099719910 created "2020-11-23" @default.
• W3099719910 creator A5050593135 @default.
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• W3099719910 date "2015-02-27" @default.
• W3099719910 modified "2023-10-14" @default.
• W3099719910 title "A Note on Colored HOMFLY Polynomials for Hyperbolic Knots from WZW Models" @default.
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• W3099719910 doi "https://doi.org/10.1007/s00220-015-2322-z" @default.
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