The non-Abelian tensor multiplet

We assume the existence of a background vector field that enables us to make an ansatz for the superconformal transformations for the non-Abelian 6d (1, 0) tensor multiplet. Closure of supersymmetry on generators of the conformal algebra and the R-symmetry, requires that the vector field is Abelian, has scaling dimension minus one and that the supersymmetry parameter as well as all the fields in the tensor multiplet have vanishing Lie derivatives along this vector field. We couple the tensor multiplet to an adjoint hypermultiplet, and present a Lagrangian for the combined system that has enhanced (2, 0) superconformal symmetry. We also obtain the off-shell supersymmetry variations for both the tensor and the hypermultiplets.