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We propose an ${\rm SU}(6)$ unified theory that solves the strong ${\it CP}$problem with a high-quality axion. This is achieved by an automatic globalPeccei-Quinn ${\rm U}(1)_{\rm PQ}$ symmetry and the gauged discrete$\mathbb{Z}_{4{\cal R}}$ symmetry. With the axion mass predictions of $m_a \sim{\cal O}(10^{-3} ) - {\cal O}(0.1) \,{\rm eV}$, as well as a universalaxion-photon coupling in the unification models, the QCD axion can be probed inthe upcoming experiments of IAXO. An intermediate gauge symmetry breaking scalecharacterized by the axion decay constant is obtained by the Peccei-Quinnquality argument, which is likely to achieve a successful leptogenesis throughthe type-I seesaw mechanism. The Higgs sector at the electroweak scale is atype-II two-Higgs-doublet model. The gauge coupling unification is possiblewith the supersymmetric extension.

Axion model with the ${\rm SU}(6)$ unification