Unified Origin of Axion and Monopole Dark Matter, and Solution to the Domain-wall Problem

We propose a scenario where the spontaneous breakdown of the Peccei-Quinn symmetry leads to monopole production. Both the axion and the monopole contribute to dark matter, and the Witten effect on the axion mass is a built-in feature. In the KSVZ-type axion model, seemingly different vacua are actually connected by the hidden gauge symmetry, which makes the axionic string unstable and separate into two Alice strings. The Alice string is attached to a single domain wall due to the QCD instanton effect, solving the domain-wall problem. This is in the same spirit of the Lazarides-Shafi mechanism, although the discrete Peccei-Quinn symmetry is not embedded into the center of the original gauge symmetry. In the DFSZ-type axion model, the domain-wall problem is avoided by the Witten effect. If the Peccei-Quinn symmetry is explicitly broken by a small amount, monopoles acquire a tiny electric charge and become mini-charged dark matter. Interestingly, the quality of the Peccei-Quinn symmetry is closely tied to darkness of dark matter.