Solving Topological Field Theories on Mapping Tori

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 Σ×S, 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. IC/95/341 hep-th/9605095 ENSLAPP-L-590/96 e-mail: [email protected]; supported by EC Human Capital and Mobility Grant ERB-CHB-GCT-93-0252 URA 14-36 du CNRS, associée à l’E.N.S. de Lyon, et à l’Université de Savoie e-mail: [email protected]; supported by EC Human Capital and Mobility Grant ERB-CHB-ICT-93-0269 e-mail: [email protected]