Traditional DHR superselection theory considers charges localized in compact regions. One can also generalize DHR theory to the case of representations localized on neighbourhoods of semi-infinite rays. This is now usually going by the term “string localization” (though there is no known relation to other uses of the word “string” in physics, except maybe the suggestion (Buchholz-Fredenhagen 82), that one can understand these rays as reflecting flux tubes? between two charged particles).
Massive interacting string-localized objects in AQFT were first considered (though not constructed) in
and reviewed for instance in
‘ Christian Köhler, String-localized fields and point-localized currents in massless Wigner representations with infinite spin, Diplom(Master) thesis (2005) (pdf)