Exact computations in topological abelian Chern-Simons and BF theories

2017/05/28 by Philippe Mathieu, Mathieu, Philippe
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1705.09945

openalex publication_date 2017/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce Deligne cohomology that classifies U(1) fibre bundles over 3-manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (non-perturbative) computations in U(1) Chern-Simons theory (resp. BF theory) at the level of functional integrals. The partition functions (and observables) of these theories are strongly related to topological invariants well-known by the mathematicians.

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