An Extra-Dimensional Axion in a 5D Warped Orbifold GUT

We study the QCD axion arising from the 5th component of a bulk $U(1)$ gauge field in a five-dimensional warped grand unified theory, and determine the viable range of the axion decay constant $f_a$. Unlike flat extra dimensions, where gauge couplings run quickly above the Kaluza--Klein (KK) scale, the logarithmic running in warped geometries permits substantially smaller $f_a$ while preserving perturbative gauge coupling unification. However, bulk tree-level contributions to the gauge coupling -- interpreted holographically as CFT renormalization -- place a lower bound on $f_a$. We find that the conventional QCD axion window $10^{9}\,\mathrm{GeV} \lesssim f_a \lesssim 10^{12}\,\mathrm{GeV}$ is readily compatible without losing perturbativity, provided the AdS curvature is near the Planck scale. Thus, the 5D warped orbifold GUT naturally accommodates a high-quality QCD axion in a grand unified theory that provides an effective description of string-theoretic warped flux compactifications, admitting complementary geometric and holographic descriptions of the axion.