Extra-dimensional axion patterns

We study the parameter space of a bulk axion in flat and warped extra spacetime dimensions. We characterize in detail the regimes where no single KK mode is produced along the canonical QCD axion line, and instead, it is maximally deviated along with several other axions that constitute a multiple solution to the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>C</a:mi><a:mi>P</a:mi></a:mrow></a:math> problem. In both flat and Randall-Sundrum scenarios, and assuming that all Peccei-Quinn breaking comes from QCD, we find that these solutions are however subject to tight phenomenological constraints. In light of these results, we expect that only KK canonical patterns (with the zero-mode close to the standard QCD line) can emerge from a bulk axion in one or more extra spacetime dimensions. As a byproduct, we generalize the axions eigenvalue and eigenvector equations for an arbitrary number of spacetime dimensions and compactifications.