Towards a UV-Model of Kinetic Mixing and Portal Matter II: Exploring Unification in an $SU(N)$ Group

If dark matter (DM) interacts with the Standard Model (SM) via the $U(1)_D$ kinetic mixing (KM) portal at low energies, it necessitates not only the existence of portal matter (PM) particles which carry both dark and SM quantum numbers, but also a possible UV completion into which this $U(1)_D$ and the SM are both embedded. In earlier work, following a bottom-up approach, we attempted to construct a more unified framework of these SM and dark sector interactions. In this paper we will instead begin to explore, from the top-down, the possibility of the unification of these forces via the decomposition of a GUT-like group, $G\to G_{SM}\times G_{Dark}$, where $U(1)_D$ is now a low energy diagonal subgroup of $G_{Dark}$ and where the familiar $G_{SM}=SU(5)$ will play the role of a proxy for the conventional $SU(3)_c\times SU(2)_L\times U(1)_Y$ SM gauge group. In particular, for this study it will be assumed that $G=SU(N)$ with $N=6-10$. Although not our main goal, models that also unify the three SM generational structure within this same general framework will also be examined. The possibilities are found to be quite highly constrained by our chosen set of model building requirements which are likely too strong when they are employed simultaneously to obtain a successful model framework.