  We use the framework of relativistic and non-relativistic conformal field
theories (CFT) to derive general results relevant for the production of weakly
coupled and strongly coupled dark sectors through thermal interactions. Our
result reproduce trivially known formulas for $2\to n $ processes and extend to
general $m\to n$ processes as well as interacting dark sectors. As concrete
examples we consider freeze-in of a relativistic CFT coupled to the SM with
contact interactions and derive Sommerfeld enhancement of non-relativistic
cross-sections from the theory of fermions at unitarity.
