Three-manifold invariant from functional integration
Mathematical Physics
2015-05-29 v1 High Energy Physics - Theory
math.MP
Abstract
We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant.
Cite
@article{arxiv.1301.6407,
title = {Three-manifold invariant from functional integration},
author = {E. Guadagnini and F. Thuillier},
journal= {arXiv preprint arXiv:1301.6407},
year = {2015}
}