English

Remarks on Chern-Simons Theory

Algebraic Topology 2008-10-28 v2 High Energy Physics - Theory Mathematical Physics Differential Geometry math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0808.2507,
  title  = {Remarks on Chern-Simons Theory},
  author = {Daniel S. Freed},
  journal= {arXiv preprint arXiv:0808.2507},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T11:11:46.709Z