MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Level in Chern-Simons theory

Kishore Marathe


The Chern-Simons theory is parametrized by a real number k called the level of the theory. In many applications one is required to restrict the level to take integral values. Formulas involving level usually consider only the positive integral values. We discuss the significance of level in different applications of the Chern-Simons theory and extend the formulas with positive integral values of k to negative integral values of k. The shift in k by the Coxter number of the gauge group must also be taken into account for negative k. In Witten's derivation of the skein relations for the family of two variable Jones polynomials by using topological quantum field theory, the negative values of the level k (suitably shifted by the dual Coxeter number of SU(n)) give the missing half of this family which contains the skein relation characterizing the original single variable Jones polynomials.

Aug 28, 2001
Aug 28, 2001

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2001 Repository Open Access
Kishore B. Marathe

Level in Chern-Simons theory