  Large classes of dark sector models feature mass scales and couplings very
different from the ones we observe in the Standard Model (SM). Moreover, in the
freeze-in mechanism, often employed by the dark sector models, it is also
required that the dark sector cannot be populated during the reheating process
like the SM. This is the so called asymmetric reheating. Such disparities in
sizes and scales often call for dynamical explanations. In this paper, we
explore a scenario in which slow evolving conformal field theories (CFTs) offer
such an explanation. Building on the recent work on conformal freeze-in (COFI),
we focus on a coupling between the Standard Model Hypercharge gauge boson and
an anti-symmetric tensor operator in the dark CFT. We present a scenario which
dynamically realizes the asymmetric reheating and COFI production. With a
detailed study of dark matter production, and taking into account limits on the
dark matter (DM) self-interaction, warm DM bound, and constraints from the
stellar evolution, we demonstrate that the correct relic abundance can be
obtained with reasonable choices of parameters. The model predicts the
existence of a dark photon as an emergent composite particle, with a small
kinetic mixing also determined by the CFT dynamics, which correlates it with
the generation of the mass scale of the dark sector. At the same time, COFI
production of dark matter is very different from those freeze-in mediated by
the dark photon. This is an example of the physics in which a realistic dark
sector model can often be much richer and with unexpected features.
