Details

Autor(en) / Beteiligte

• Gu, Jie
• Jockers, Hans

Titel

A Note on Colored HOMFLY Polynomials for Hyperbolic Knots from WZW Models

Ist Teil von

• Communications in mathematical physics, 2015-08, Vol.338 (1), p.393-456

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2015

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 U q s u ( 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.