Axion in the minimal SO(10) GUT

The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets $\mathbf{10}$ and $\overline{\mathbf{126}}$. The relative phase between the VEVs of $(\mathbf{10},\mathbf{1},\mathbf{3})\subset \overline{\mathbf{126}}$ and $(\overline{\mathbf{10}},\mathbf{1},\mathbf{3})\subset \mathbf{126}$ under $\mathrm{S}\mathrm{U}(4{)}_C\times \mathrm{S}\mathrm{U}(2{)}_L\times \mathrm{S}\mathrm{U}(2{)}_R$ is identified with the axion. The Peccei-Quinn and $B-L$ symmetry breaking scales coincide through $\mathrm{\mid }⟨{\mathrm{\Delta }}_R⟩\mathrm{\mid }=\mathrm{\mid }⟨{\bar{\mathrm{\Delta }}}_R⟩\mathrm{\mid }$. The scalar partner of the lightest right-handed neutrino plays the role of the inflaton, realizing hybrid inflation consistent with the observed CMB density fluctuations. After inflation, both fields acquire VEVs, and the domain-wall problem is resolved through the Lazarides-Shafi mechanism, which naturally restricts the model to three generations.