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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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Orientability of moduli space and determinant bundle of ASD operator

You want a line bundle that's well-defined over the entire space of irreducible connections $\mathcal B^*$; this is how you see, for instance, that a choice of orientation at one point in the moduli s …
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5 votes

When is the action of the gauge group on the space of connections free?

It suffices that there is a straight line (identified with $\Bbb R$ below) in $\Bbb R^4$ so that the connection matrix $A$ is $L^1$ (with respect to the trivial connection) when restricted to that lin …
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