Eliminativism and the QCD \(\theta _{\text {YM}}\)-Term: What Gauge Transformations Cannot Do

The eliminative view of gauge degrees of freedom—the view that they arise solely from descriptive redundancy and are therefore eliminable from the theory—is a lively topic of debate in the philosophy of physics. Recent work attempts to leverage properties of the QCD \(\theta _{\text {YM}}\)-term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD \(\theta _{\text {YM}}\)-term changes under “large” gauge transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the \(\theta _{\text {YM}}\)-term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is fully gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the \(\theta _{\text {YM}}\)-term shows the physical importance of bundle topology (or superpositions thereof) and thus counts against (a naive) eliminativism.