A high quality composite axion

Abstract The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N) L × SU(N) × SU(N) R × U(1) X product gauge group, achieving θ ¯ $$ \left|\overline{\uptheta}\right| $$ < 10−11 for an SU(5) model with f a ≲ 3 × 1011 GeV. This construction leads to low energy predictions such as a U(1) X gauge symmetry, and for X = B − L engineers a naturally O $$ \mathcal{O} $$ (TeV) value for the μ parameter of the MSSM.