Accidental Peccei-Quinn Symmetry Protected to Arbitrary Order

A SU(N)L×SU(N)R gauge theory for a scalar multiplet Y transforming in the bifundamental representation (N,N̄) preserves, for $N>4$, an accidental $U(1)$ symmetry first broken at operator dimension N. A vacuum expectation value for Y can break the symmetry to Hₛ=SU(N)L+R or to Hₕ=0ex0exSU(N-1)L×SU(N-1)R×U(1)L+R. In the first case the accidental $U(1)$ gets also broken, yielding a pseudo-Nambu-Goldstone boson with mass suppression controlled by N. In the second case a global $U(1)$ remains unbroken. The strong $CP$ problem is solved by coupling Y to new fermions carrying color. The first case allows for a Peccei-Quinn solution with U(1)PQ protected by the gauge symmetry up to order N. In the second case $U(1)$ can get broken by condensates of the new strong dynamics, resulting in a composite axion. By coupling Y to fermions carrying only weak isospin, models for axionlike particles can be constructed.