Exact computations in topological abelian Chern-Simons and BF theories
Philippe Mathieu
TL;DR
This paper introduces Deligne cohomology as a tool for exact, non-perturbative calculations in U(1) Chern-Simons and BF theories, linking quantum field theory to topological invariants.
Contribution
It demonstrates how Deligne cohomology enables precise computations of partition functions and observables in topological gauge theories.
Findings
Exact computations of partition functions achieved
Connection established between field theory and topological invariants
Framework applicable to 3-manifolds with connections
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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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics