High-quality grand unified theories with three generations

TL;DR

This paper explores extended gauge groups beyond SU(5) and SU(6) to construct grand unified theories that naturally produce three generations of Standard Model fermions, addressing anomaly cancellation and the PQ problem.

Contribution

It identifies new candidate gauge groups (SU(7), SU(8), SU(9), SU(10), SU(11)) capable of generating three fermion generations and solving the PQ quality problem within GUT frameworks.

Findings

SU(7), SU(8), SU(9) are asymptotically free and anomaly-free.

SU(10) and SU(11) can produce three generations without asymptotic freedom.

Models can inherently solve the PQ quality problem.

Abstract

We extend the unitary groups beyond the ${\rm SU}(5)$ and ${\rm SU}(6)$ 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 ${\rm SU}(7)$, ${\rm SU}(8)$ and ${\rm SU}(9)$ together with their anomaly-free irreducible representations are such candidates. Two additional gauge groups of ${\rm SU}(10)$ and ${\rm SU}(11)$ 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.