TL;DR
This paper explores the connection between Chern-Simons forms and harmonic forms on principal bundles, revealing that under certain conditions, the Chern-Simons 3-form becomes harmonic in the adiabatic limit.
Contribution
It establishes a relationship between Chern-Simons forms and harmonic forms on principal bundles using the adiabatic limit, under specific assumptions about the structure group.
Findings
Chern-Simons 3-form is harmonic in the adiabatic limit for simple G.
The relationship involves an exact Chern-Weil 4-form.
Harmonicity is achieved after subtracting a canonical base term.
Abstract
We show a relationship between Chern-Simons 1- and 3-forms and harmonic forms on a principal bundle. Doing so requires one to consider an adiabatic limit. For the 3-form case, assume that G is simple and the corresponding Chern-Weil 4-form is exact. Then, the Chern-Simons 3-form on the princpal bundle G-bundle, minus a canonical term from the base, is harmonic in the adiabatic limit.
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