Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets

We construe six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2, 0) theories, coupled to (11, 0) vector nmltiplets. The latter are part of the non-abelian gauge structure that also includes non-dynamical three- and four-forms. The hypernmltiplets are described by gauged nonlinear sigma models with a hyper-Kahler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.