  In this paper we study segmented strings in AdS$_3$ coupled to a background
two-form whose field strength is proportional to the volume form. By changing
the coupling, the theory interpolates between the Nambu-Goto string and the
$SL(2)$ Wess-Zumino-Witten model. In terms of the kink momentum vectors, the
action is independent of the coupling and the classical theory reduces to a
single discrete-time Toda-type theory. The WZW model is a singular point in
coupling space where the map into Toda variables degenerates.
