Constructing $SU(N)$ strongly coupled dark sectors by extending the Standard Model: mixed representations, flavor structure, global symmetries and various portals

Motivated by the potential existence of a dark QCD sector, we construct a $SU(N)$ strongly coupled dark sector by extending the Standard Model (SM) gauge group to an enlarged $SU(N+5)\times SU(N+1)\times U(1)$, under which the dark quark candidates naturally arises from the same multiplets as the SM fermions. The dark QCD sector from the extension inherits the rich structure of the SM, featuring three distinct properties: (1) Mixed representations: There are dark quarks of three different representations, including fundamental (${\chi }_f$), antisymmetric (${\chi }_a$), and symmetric (${\chi }_s$), which can be traced back to the chiral structure of the SM. (2) Flavor: Each representation features three generations, with their flavor structures and Yukawa interactions directly related to those of the SM. (3) Global symmetries: Alongside the conventional dark baryon number $D$, we identify an exotic dark baryon number $\tilde{D}$ from a conserved $(B-L)-\tilde{D}$ symmetry. These features provide novel perspectives on the structure of dark QCD sectors. Furthermore, the extension of the scalar and gauge sectors introduces various portals between the dark QCD sector and the SM sector. We systematically study these portals, including quark portal, lepton portal, Higgs and $Z$ portal, heavy $Z^{\mathrm{\prime }}$ portal, kinetic mixing portal, dipole portal, and dark pion/axion portals. With a concrete UV model, their origin become robust, providing additional guidance for experimental searches of the dark sector.