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 ${\bf 10}$ and $\overline{{\bf 126}}$. The relative phase between the VEVs of $({\bf 10,1,3})\subset\overline{{\bf 126}}$ and $({\bf \overline{10},1,3})\subset{\bf 126}$ under ${\rm SU}(4)_C\times{\rm SU}(2)_L\times{\rm SU}(2)_R$ is identified with the axion. The Peccei-Quinn and $B-L$ symmetry breaking scales coincide through $|\langle\Delta_R\rangle|=|\langle\overline{\Delta}_R\rangle|$. 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.