Explicit R and Racah matrices are given for the symmetric representation of SO(5) to compute Kauffman polynomials via a generalized Reshetikhin-Turaev construction.
Chern-Simons Invariants of Torus Links
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abstract
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
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hep-th 3representative citing papers
HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.
For p-party pure states from T_{p,p} torus link complements in SU(2)_k Chern-Simons theory, the characteristic polynomials of (1|p-1)-reduced density matrices are monic polynomials with rational coefficients.
citing papers explorer
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Racah matrices for the symmetric representation of the SO(5) group
Explicit R and Racah matrices are given for the symmetric representation of SO(5) to compute Kauffman polynomials via a generalized Reshetikhin-Turaev construction.
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A relation between the HOMFLY-PT and Kauffman polynomials via characters
HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.
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Analyzing reduced density matrices in SU(2) Chern-Simons theory
For p-party pure states from T_{p,p} torus link complements in SU(2)_k Chern-Simons theory, the characteristic polynomials of (1|p-1)-reduced density matrices are monic polynomials with rational coefficients.