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Quantum field theory and the Jones polynomial

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Abstract

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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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, Olden Lane, 08540, Princeton, NJ, USA

    Edward Witten

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  1. Edward Witten
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Additional information

Communicated by A. Jaffe

An expanded version of a lecture at the IAMP Congress, Swansea, July, 1988

Research supported in part by NSF Grant No. 86-20266, and NSF Waterman Grant 88–17521

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Witten, E. Quantum field theory and the Jones polynomial. Commun.Math. Phys. 121, 351–399 (1989). https://doi.org/10.1007/BF01217730

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