Consequences of Multiple Axions in Theories with Dark Yang-Mills Groups

General consistency requirements of Quantum Gravity demand the existence of one axion per Yang-Mills group. In this work, we consider theories with dark Yang-Mills sectors and investigate general phenomenological implications of these necessary axions. We carry out computations for two simple models, namely a pure Yang-Mills sector and $N$ exact Standard Model copies. For the former, the misalignment mechanism results in a minimal dark confinement scale $\Lambda_{\rm conf} \gtrsim 1 \, {\rm eV}$ if the dark sector axion is supposed to make up the dark matter. For the latter, the misalignment mechanism without fine-tuning of the initial misalignment angle places an upper bound on $N$ below the species bound. When the PQ symmetries are broken during inflation, the collective isocurvature fluctuations do not necessarily tighten the bound on the inflationary Hubble scale arising from a single axion. We also point out that axion stars collectively made from axions of different dark sectors with a suppressed mass spectrum are not possible. Lastly, for the two models at hand, intersector interaction through axion kinetic mixing leads to the existence of two distinct axion states. For a single dark YM sector, the upper bound $\Lambda_{\rm conf} \lesssim 10^{12} \, {\rm GeV}$ emerges from the stability requirement of the dark sector axion. For $N$ exact SM copies, the mass and photon coupling of the second state is completely determined after a potential measurement of the analogous parameters of the first axion.