Extra-Dimensional Axion Expectations

Axions arising as modes of higher-dimensional gauge fields are known to offer a compelling solution to the axion quality problem and to naturally arise in string theory. In this context, it is interesting to ask how we would interpret an experimental measurement of the axion decay constant $f$. I give several arguments for, as well as concrete examples in string theory of, the existence in such a model of an axion string with tension of order $2\pi S_\mathrm{inst} f^2$, where $S_\mathrm{inst}$ is the instanton action. Furthermore, in models of this type axion strings are typically fundamental objects (rather than solitons), whose tension is at or above the fundamental cutoff of the theory. As a result, I argue that for an extra-dimensional QCD axion, it is likely that the fundamental cutoff scale lies at most two orders of magnitude above $f$. In addition to these core arguments, this paper begins with a self-contained introduction to the physics of extra-dimensional axions and ends with some comments on axion physics in relation to chiral fermions.