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Advances in High Energy Physics
Volume 2017, Article ID 2878949, 6 pages
https://doi.org/10.1155/2017/2878949
Research Article

Exact Computations in Topological Abelian Chern-Simons and BF Theories

LAPTh, Université de Savoie, CNRS, Chemin de Bellevue, BP 110, 74941 Annecy-le-Vieux Cedex, France

Correspondence should be addressed to Philippe Mathieu; rf.srnc.htpal@ueihtam.eppilihp

Received 15 May 2017; Accepted 18 June 2017; Published 30 August 2017

Academic Editor: Ralf Hofmann

Copyright © 2017 Philippe Mathieu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We introduce Deligne cohomology that classifies fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in Chern-Simons theory (BF theory, resp.) at the level of functional integrals. The partition functions (and observables) of these theories are strongly related to topological invariants well known to the mathematicians.