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.

💡 Research Summary

The paper investigates a QCD axion that originates from the fifth component (A_5) of a bulk U(1) gauge field in a five‑dimensional warped grand‑unified theory (GUT). The authors embed a supersymmetric SU(5) GUT and a separate U(1)(_C) vector supermultiplet in a slice of AdS(_5) with an (S^1/Z_2) orbifold. The Standard Model matter and Higgs fields live on the UV brane, while the bulk hosts the gauge multiplets. In this setup the 5‑dimensional gauge field’s zero‑mode provides a pseudo‑Nambu‑Goldstone boson with a 2π periodicity, identified as the QCD axion.

A central technical point is the renormalization‑group (RG) evolution of the four‑dimensional effective gauge couplings. In flat extra dimensions the tower of Kaluza‑Klein (KK) states induces a power‑law running, forcing the first KK mass to lie near the unification scale and consequently imposing a very high lower bound on the axion decay constant ((f_a \gtrsim 10^{14}) GeV). By contrast, in a warped background the 5D gauge coupling (g_5) scales with the AdS curvature (k), and the 4D couplings run only logarithmically even above the KK threshold. The running receives two contributions: the usual MSSM beta‑function term (b_i) and an additional universal term (b_{\rm CFT}=8\pi^2/(k g_5^2)) that can be interpreted holographically as the contribution of a large‑(N) conformal field theory (CFT) dual to the bulk gauge sector.

The axion decay constant is set by the higher‑dimensional gauge coupling and the geometry:
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