1993/05/24 by G.E. Thompson, George Thompson, Thompson, George · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9305120
70 A4 pages (LaTex, 6 figures not included), IC/93/112
arxiv created 1993/05/24 · openalex publication_date 1993/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In these lecture notes we explain a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called BF and cohomological theories. The quantum Yang-Mills theory is solved exactly using path integral techniques. Explicit expressions, in terms of group representation theory, are obtained for the partition function and various correlation functions. In a particular limit the Yang-Mills theory devolves to the topological models and the previously determined correlation functions give topological information about the moduli spaces of flat connections. In particular, the partition function yields the volume of the moduli space for which an explicit expression is derived. These notes are self contained, with a basic introduction to the various ideas underlying the topological field theories. This includes some relatively new work on handling problems that arise in the presence of reducible connections which in turn forms the bridge between the various models under consideration. These notes are identical to those made available to participants of the 1992 summer school in Trieste, except for one or two additions added circa January 1993.