Intersection Pairings on Spaces of Connections and Chern-Simons Theory on Seifert Manifolds

Abstract

Let M be a U(1) bundle over a smooth Riemann surface. I show that for Chern-Simons theory on M, with structure group G, the path integral is an integral over the space of G-connections on the Riemann surface involving characteristic classes as well as a certain 4-dimensional class that comes from a universal bundle. When M is the product of a Riemann surface with a circle the 4-dimensional class does not enter and the path integral takes the form of a Riemann-Roch formula albeit in infinite dimensions. The discussion is generalised to include Wilson lines along the fibre direction in M.

Talk given at the workshop Chern-Simons Gauge Theory: 20 years after, August 3-7 2009, Hausdorff Center for Mathematics, 13 pages

References in corpus (2)

• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Localization for Wilson Loops in Chern-Simons Theory

Cited by in corpus (3)

• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Chern-Simons Theory on Seifert 3-Manifolds
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement