The 3-lie algebra (2,0) tensor multiplet and equations of motion on loop space

We show that a recently found set of supersymmetric equations of motion for a 3-Lie algebra-valued (2,0) tensor multiplet finds a natural interpretation as supersymmetric gauge field equations on loop space. We find that BPS solutions to these equations yield a previously proposed nonabelian extension of the selfdual string. We describe an ADHMN-like construction that allows for the explicit construction of such BPS solutions.