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Gauge theory in physics and mathematics refers to a field theory whose fields include principal bundles with connection.
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Is a closed basic 2-form on a principal $S^1$ bundle the curvature of a connection?
Suppose one has an $S^1$ principal bundle $p: P\rightarrow M$, and a closed 2-form $F$ on $M$. Then the pullback form $p^*F$ is closed, vanishes on vertical vectors, and is invariant under the action …