Consequences of multiple axions in theories with dark Yang-Mills groups

General consistency requirements of quantum gravity suggest the existence of one axion per Yang-Mills group (YM) [a gauged special unitary group SU(n)]. In this work we take this requirement seriously and consider theories with dark Yang-Mills sectors and investigate general phenomenological implications of these axions. We carry out computations for two simple models, namely a pure Yang-Mills sector and N exact Standard Model (SM) copies. For the former, the misalignment mechanism results in a minimal dark confinement scale Lambda conf greater than or similar to 1 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 Peccei-Quinn 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 conf less than or similar to 1012 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.