  We present an interacting action that lives in loop space, and we argue that
this is a generalization of the theory for a free tensor multiplet. From this
action we derive the Bogomolnyi equation corresponding to solitonic strings.
Using the Hopf map, we find a correspondence between BPS strings and BPS
monopoles in four-dimensional super Yang-Mills theory. This enable us to find
explicit BPS saturated solitonic string solutions.
