$SU(3)^p$ Quiver Theories with ${\cal N} = 0$ for $p=8$ and $9$

Abstract

We close a gap in previous studies of nonsupersymmetric ${\cal N}=0$ quiver gauge theories from a phenomenological point of view aimed at acquiring specific proposals for models beyond the Standard Model (BSM). Because $SU(3)$ is the gauge group of QCD we fix $N=3$ and vary only the $Z_p$ abelian orbifold. The values $1 \leq p \leq 7$ have been previously fully discussed as well as one special case, discovered by happenstance, of $p=12$. The values $p = 8$ and $p=9$ are discussed comprehensively in the present paper including the electroweak mixing angle, gauge coupling unification, spontaneous symmetry breakdown to the standard model, and the occurrence of three quark-lepton families. Two promising quiver node identifications are discovered for $p=8$ and three for $p=9$. All of these merit further study as BSM candidates.