Remarks on Chern-Simons Theory

Details Remarks on Chern-Simons Theory Remarks on Chern-Simons Theory

2008-08-19

arxiv.org/abs/0808.2507v2

Mathematics

Algebraic Topology

34 pages, 1 figure, based on talk at 25th anniversary conference for MSRI; minor revisions

Scientific paper

In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has served as a key example in understanding the structure of TQFTs in general. We survey some of that structure with a particular focus on the "multi-tier" aspects. We discuss general axioms, generators-and-relations theorems, a priori constructions, dimensional reduction and K-theory, and Chern-Simons as a 0-1-2-3 theory. An appendix gives a lightening treatment of the Chern-Simons-Weil theory of connections. The paper concludes with general remarks about the Geometry-QFT-Strings interaction.

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