CP alone allows the QCD theta angle to be 0 or pi; choosing a gauge group with enlarged theta periodicity forces CP to select 0, eliminating the excluded pi value.
Parity solves the Strong CP problem
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abstract
A recent paper "What can solve the strong CP problem?" goes counter to conventional wisdom by arguing that the universe was in an initial state that combines different eigenstates of $\theta$ (of the theta vacuum of QCD), and asserts that for such an initial state, axionless solutions to the Strong CP Problem based on P and CP symmetries will not work. We discuss the nature of the theta vacuum in light of this work, and find that the conventional framing and solutions based on P and CP symmetries are on a firm footing.
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When CP requires $\bar\theta=0$, not $\bar\theta=\pi$
CP alone allows the QCD theta angle to be 0 or pi; choosing a gauge group with enlarged theta periodicity forces CP to select 0, eliminating the excluded pi value.