Accidental Peccei-Quinn symmetry protected to arbitrary order (1704.01122v1)

Abstract: A $SU(N)L\times SU(N)_R$ gauge theory for a scalar multiplet $Y$ transforming in the bi-fundamental representation $(N,\bar N)$ preserves, for $N>4$, an accidental $U(1)$ symmetry firstly broken at operator dimension $N$. Two configurations are possible for the vacuum expectation value of $Y$, which correspond to the (maximal) little groups $\mathcal{H}_s=SU(N){L+R}$ and $\mathcal{H}h=SU(N-1)_L\times SU(N-1)_R\times U(1){L+R}$. In the first case the accidental $U(1)$ gets also broken, yielding a pseudo Nambu-Goldstone boson with mass suppression controlled by $N$, while 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 up to order $N$ by the gauge symmetry. 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 axion-like particles can be constructed.