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Chern-Simons Invariants of Torus Links

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arxiv 1003.2861 v2 pith:SUWLSQMC submitted 2010-03-15 hep-th math.GTmath.QA

Sébastien Stevan This is my paper · ORCID
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keywords invariantsformulatoruschern-simonshomflykauffmanlinksobtain
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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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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Racah matrices for the symmetric representation of the SO(5) group

    hep-th 2026-03 unverdicted novelty 7.0 of 10

    Explicit R and Racah matrices are given for the symmetric representation of SO(5) to compute Kauffman polynomials via a generalized Reshetikhin-Turaev construction.

  2. A relation between the HOMFLY-PT and Kauffman polynomials via characters

    hep-th 2026-03 conditional novelty 7.0 of 10

    HOMFLY-PT/Kauffman relation via BMW characters proves HZ factorisability for 3-strand knots but fails for 4-strand knots.

  3. Torus knots in adjoint representation and Vogel's universality

    hep-th 2025-06 conditional novelty 6.0 of 10

    Universal adjoint invariants for T[4,n] torus knots are constructed via Vogel's universality, completing the T[4,n] case after previous T[2,n] and T[3,n] results.

  4. The HOMFLY-PT polynomial and HZ factorisation

    math-ph 2024-12 conditional novelty 6.0 of 10

    The HOMFLY-PT and Kauffman polynomials satisfy a previously torus-only relation for several infinite hyperbolic knot families that have factorised Harer-Zagier transforms.

  5. Large-party limit of topological entanglement entropy in Chern-Simons theory

    hep-th 2026-01 conditional novelty 5.0 of 10

    As the number of parties d grows to infinity, the entanglement entropy of Chern-Simons torus-link states is carried only by Abelian anyons and is bounded above by ln|Z_G|.

  6. Analyzing reduced density matrices in SU(2) Chern-Simons theory

    hep-th 2025-04 unverdicted novelty 4.0 of 10

    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.

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