nLab Jones polynomial as Wilson loop observable -- references

Jones polynomial as Wilson loop observables

The identification of the Jones polynomial with Wilson loop observables in Chern-Simons theory is due to

• Edward Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121,351-399 (1989) (euclid.cmp/1104178138)

see also

• Jürg Fröhlich, C. King, The Chern-Simons theory and knot polynomials, Comm. Math. Phys.

  Volume 126, Number 1 (1989), 167-199 (euclid.cmp/1104179728)

Lecture notes:

• Edward Witten, A New Look At The Jones Polynomial of a Knot, Clay Conference, Oxford, October 1, 2013 (pdf)

The categorification of this relation to an identification of Khovanov homology with observables in D=4 super Yang-Mills theory:

• Edward Witten, Khovanov homology and gauge theory, arxiv/1108.3103

• Edward Witten, Fivebranes and Knots (arXiv:1101.3216)

Lecture notes:

• Edward Witten, Khovanov Homology And Gauge Theory, Clay Conference, Oxford, October 2, 2013 (pdf)

See also:

• Vaughan Jones, Index for subfactors, Invent. Math. 72, I (I983); A polynomial invariant for links via yon Neumann algebras, Bull. AMS 12, 103 (1985); Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126, 335 (1987)

Via factorization homology:

• Kevin Costello, John Francis, Owen Gwilliam: Chern-Simons factorization algebras and knot polynomials [arXiv:2602.12412]