Solving Topological Field Theories on Mapping Tori

Abstract

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1|1) model of Rozansky and Saleur on $\Sigma x{S}^1$, both directly and using equivalent two-dimensional theories. We also derive the partition function of a certain non-abelian generalization of the U(1|1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two-dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold.

16 pages, LaTeX file

References in corpus (6)

• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• On Diagonalization in Map(M,G)
• Reidemeister torsion, the Alexander polynomial and $U(1,1)$ Chern-Simons theory
• Equivariant Kaehler Geometry and Localization in the G/G Model
• Seiberg-Witten Floer Homology and Heegaard Splittings

Cited by in corpus (1)

• Massive Ray-Singer Torsion and Path Integrals