Remarks on Chern-Simons Theory

2008/08/19 by Daniel S. Freed, Freed, Daniel S. · 2 citations
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0808.2507

openalex publication_date 2008/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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