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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>N</a:mi></a:mrow></a:math> exact Standard Model (SM) copies. For the former, the misalignment mechanism results in a minimal dark confinement scale <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi mathvariant="normal">Λ</c:mi><c:mrow><c:mi>conf</c:mi></c:mrow></c:msub><c:mo>≳</c:mo><c:mn>1</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>eV</c:mi></c:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>N</f:mi></f:math> 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 <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi mathvariant="normal">Λ</h:mi><h:mrow><h:mi>conf</h:mi></h:mrow></h:msub><h:mo>≲</h:mo><h:msup><h:mn>10</h:mn><h:mn>12</h:mn></h:msup><h:mtext> </h:mtext><h:mtext> </h:mtext><h:mi>GeV</h:mi></h:math> emerges from the stability requirement of the dark sector axion. For <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>N</k:mi></k:math> 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.