  New dark sectors consisting of exotic fields that couple only very feebly to
the Standard Model (SM) have strong theoretical motivation and may be relevant
to explaining the abundance of dark matter (DM). An important question for such
sectors is how they connect to the SM. For a dark sector with a new gauge
interaction, a natural connection arises from heavy vector-like fermions
charged under both the visible and dark gauge groups. The gauge charges of such
fermions imply that one or more of them is stable in the absence of additional
sources of dark symmetry breaking. A generic challenge for such connectors is
that they can produce too much dark matter or interact too strongly with nuclei
if they were ever thermalized in the early universe. In this paper we study
this challenge in a simple connector theory consisting of new vector-like
electroweak doublet and singlet fermions that also transform under the
fundamental representation of a new (Abelian) gauge force, and we show that
these connectors in their minimal form are almost always ruled out by existing
direct DM searches. To address this challenge, we investigate two solutions.
First, we study mitigating scattering on nuclei by introducing a Majorana mass
term for the singlet. And second, we investigate a mixing with SM leptons that
allows the connectors to decay while remaining consistent with cosmological
tests and searches for charged lepton flavor violation. Both solutions rely on
the presence of a dark Higgs field with a specific charge.
