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Description
After reviewing the construction of θ-vacuum states and the associated topological features in gauge theories, I will discuss physical implications that can be inferred on general grounds. In particular, the spectral asymmetry of the Dirac operator leads to the spontaneous breaking of an anomalous symmetry. This breaking is realized in the Higgs regime and gives rise to an emergent particle state. Applying this line of reasoning to the Standard Model, we predict the existence of an emergent particle state, the electroweak ηw, which can be viewed as the electroweak counterpart of the η′ meson in QCD. Parts of the talk are intentionally pedagogical, aimed at a student audience, and address recent claims that the θ-parameter does not contribute to CP-violating observables.