SU(N) quantum Racah coefficients & non-torus links
arXiv:1107.3918
Abstract
It is well-known that the SU(2) quantum Racah coefficients or the Wigner symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory. Using isotopy equivalence of SU(N) Chern-Simons functional integrals over three balls with one or more boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N) representations. Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links. These results are useful for verifying conjectures in topological string theory.
41 pages, 9 figures, Latex file, few typos corrected, added appendices of data in arXiv 1209.1346, added references,to appear in Nuclear Physics B
References in corpus (4)
Cited by in corpus (28)
- Non-abelian symmetries in tensor networks: a quantum symmetry space approach
- HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
- Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
- Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
- Character expansion for HOMFLY polynomials. I. Integrability and difference equations
- Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids
- Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
- Towards effective topological field theory for knots
- On colored HOMFLY polynomials for twist knots
- Colored knot polynomials. HOMFLY in representation [2,1]
- Knot invariants from Virasoro related representation and pretzel knots
- Towards topological quantum computer
- Equations on knot polynomials and 3d/5d duality
- Towards matrix model representation of HOMFLY polynomials
- S-duality as a beta-deformed Fourier transform
- Reformulated invariants for non-torus knots and links
- Torus HOMFLY as the Hall-Littlewood Polynomials
- Racah matrices and hidden integrability in evolution of knots
- Differential expansion and rectangular HOMFLY for the figure eight knot
- On R-matrix approaches to knot invariants
- On possible existence of HOMFLY polynomials for virtual knots
- Quantum Racah matrices and 3-strand braids in representation [3,3]
- Colored HOMFLY polynomials from Chern-Simons theory
- Colored Alexander polynomials and KP hierarchy
- On matrix-model approach to simplified Khovanov-Rozansky calculus
- Faces of matrix models
- Revisiting the Melvin-Morton-Rozansky Expansion, or There and Back Again
- Level-rank duality of knot and link invariants