Search for QCD Axions in light of String Theory

Abstract: The QCD axion stands as one of the most promising candidates for resolving the strong CP problem. However, the value of the axion's decay constant $f_a$ and, by extension, its mass $m_a$, remain uncertain within the framework of effective field theory, posing a challenge for experimental detection. Fortunately, fields such as cosmology and astrophysics can offer crucial clues about potential mass ranges. Additionally, string theory and the more recent swampland principles might shed some light on the subject. The most straightforward string theory compactifications suggest that $f_a$ is around the GUT scale, leading to a quantum abundance of dark matter. We found that this range can be detected through hydrogen atomic transitions. The recent concept of the dark dimension scenario introduces an alternative possibility. If axions are confined to the four-dimensional Standard Model brane, their decay constant $f_a$ would be on the order of $10^{10}$ GeV. In this scenario, where axions constitute only a minor portion of dark matter, we show that a laser-interferometry setup would be an effective detection method.