Phase and Scaling Properties of Determinants Arising in Topological Field Theories

Details Phase and Scaling Properties of Determinants Arising in Topological Field Theories Phase and Scaling Properties of Determinants Arising in Topological Field Theories

1995-06-12

arxiv.org/abs/hep-th/9506079v1

Phys.Lett. B353 (1995) 495-500

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Latex. To appear in Physics Letters B

Scientific paper

10.1016/0370-2693(95)00590-H

In topological field theories determinants of maps with negative as well as positive eigenvalues arise. We give a generalisation of the zeta-regularisation technique to derive expressions for the phase and scaling-dependence of these determinants. For theories on odd-dimensional manifolds a simple formula for the scaling dependence is obtained in terms of the dimensions of certain cohomology spaces. This enables a non-perturbative feature of Chern-Simons gauge theory to be reproduced by path-integral methods.

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