Accidental Peccei-Quinn Symmetry Protected to Arbitrary Order

A SU(N)(L) x SU(N)(R) gauge theory for a scalar multiplet Y transforming in the bifundamental representation (N, (N) over bar) 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 H-s = SU(N)(L+R) or to H-h = SU(N - 1)(L) x SU(N - 1)(R) x 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.