Axion in the minimal SO(10) GUT

A bstract The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets 10 and $$ \overline{\textbf{126}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>126</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . The relative phase between the VEVs of ( 10 , 1 , 3 ) ⊂ $$ \overline{\textbf{126}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>126</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> and ( $$ \overline{\textbf{10}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mn>10</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , 1 , 3 ) ⊂ 126 under SU(4) C × SU(2) L × SU(2) R is identified with the axion. The axion is dominantly the relative phase between ∆ R and $$ {\overline{\Delta }}_R $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mtext>∆</mml:mtext> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>R</mml:mi> </mml:msub> </mml:math> , with a small 10 -Higgs component due to the VEV hierarchy. The Peccei-Quinn and B − L symmetry breaking scales coincide through $$ \left|\left\langle {\Delta}_R\right\rangle \right|=\left|\left\langle {\overline{\Delta}}_R\right\rangle \right| $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mfenced> <mml:msub> <mml:mi>Δ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:mfenced> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mfenced> <mml:msub> <mml:mover> <mml:mi>Δ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>R</mml:mi> </mml:msub> </mml:mfenced> </mml:mfenced> </mml:math> . 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.