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,N) 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=SU(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