Communications in Mathematical Physics

, Volume 121, Issue 3, pp 351-399

First online:

Quantum field theory and the Jones polynomial

  • Edward WittenAffiliated withSchool of Natural Sciences, Institute for Advanced Study

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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.