High-quality axions in a class of chiral $U(1)$ gauge theories

We show that there are many candidates for the quintessence and/or the QCD axions in a class of chiral $U(1)$ gauge theories. Their qualities are high enough to serve as the dark energy and/or to solve the strong CP problem. Interestingly, the high quality of axion is guaranteed by the gauged $U(1)$ and $\mathbf{Z}_{2N}$ symmetries and hence free from the non-perturbative quantum gravity corrections. Furthermore, our mechanism can be easily applied to the Fuzzy dark matter axion scenarios.