Chiral models of composite axions and accidental Peccei-Quinn symmetry

We introduce a class of composite axion models that provide a natural solution to the strong CP problem, and possibly account for the observed dark matter abundance. The QCD axion arises as a composite Nambu-Goldstone boson (NGB) from the dynamics of a chiral gauge theory with a strongly-interacting and confining SU(N) factor and a weakly-interacting U(1), with no fundamental scalar fields. The Peccei-Quinn (PQ) symmetry is accidental and all the mass scales are generated dynamically. We analyze specific models where the PQ symmetry is broken only by operators of dimension 12 or higher. We also classify several other models where the PQ symmetry can be potentially protected up to the dimension 15 or 18 level. Our framework can be easily extended to a scenario where the Standard Model (SM) is unified into a simple gauge group, and we discuss the case of non-supersymmetric SU(5) unification. The GUT models predict the existence of additional pseudo NGBs, parametrically lighter than the GUT and PQ scales, which could have an impact on the cosmological evolution and leave observable signatures. We also clarify the selection rules under which higher-dimensional PQ-violating operators can generate a potential for the axion in the IR, and provide a discussion of the discrete symmetries in composite axion models associated to the number of domain walls. These results can be of general interest for composite axion models based on a QCD-like confining gauge group.