Communications in Mathematical Physics

, Volume 121, Issue 3, pp 351–399

Quantum field theory and the Jones polynomial


  • Edward Witten
    • School of Natural SciencesInstitute for Advanced Study

DOI: 10.1007/BF01217730

Cite this article as:
Witten, E. Commun.Math. Phys. (1989) 121: 351. doi:10.1007/BF01217730


It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS 3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

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© Springer-Verlag 1989