Transporters are only at the very first step of evolution. - conjecture. We know what we’d like to accomplish, but we haven’t got a clue what physics we’ll even need to learn about. The closest topic to a transporter that we do have some understanding of is wormholes.
Is this subject being studied?
Because this subject is much less developed than the search for gravity control or hyperfast propulsion, there is little or no work being directly aimed at the question of "Transporters."