High-quality grand unified theories with three generations

Abstract

We extend the unitary groups beyond the $\mathrm{SU}(5)$ and $\mathrm{SU}(6)$ to look for possible grand unified theories that give rise to three-generational Standard Model fermions without the simple repetition. By demanding asymptotic free theories at short distances, we find gauge groups of $\mathrm{SU}(7)$, $\mathrm{SU}(8)$ and $\mathrm{SU}(9)$ together with their anomaly-free irreducible representations are such candidates. Two additional gauge groups of $\mathrm{SU}(10)$ and $\mathrm{SU}(11)$ can also achieve the generational structure without asymptotic freedom. We also find these models can solve the Peccei-Quinn (PQ) quality problem which is intrinsic in the axion models, with the leading PQ-breaking operators determined from the symmetry requirement.

Comments: 20 pages, 6 tables, matches the published version