Phase and Scaling Properties of Determinants Arising in Topological Field Theories
arXiv:hep-th/9506079 · doi:10.1016/0370-2693(95)00590-H
Abstract
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.
12 pages, Latex. To appear in Physics Letters B