N=1 non-Abelian tensor multiplet in four dimensions

We carry out the $N=1$ supersymmetrization of a physical non-Abelian tensor with nontrivial consistent couplings in four dimensions. Our system has three multiplets: (i) The usual non-Abelian vector multiplet $(A_{\ensuremath{\mu}}{}^{I},{\ensuremath{\lambda}}^{I})$, (ii) A non-Abelian tensor multiplet (TM) $(B_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I},{\ensuremath{\chi}}^{I},{\ensuremath{\varphi}}^{I})$, and (iii) A compensator vector multiplet (CVM) $(C_{\ensuremath{\mu}}{}^{I},{\ensuremath{\rho}}^{I})$. All of these multiplets are in the adjoint representation of a non-Abelian group $G$. Unlike topological theory, all of our fields are propagating with kinetic terms. The $C_{\ensuremath{\mu}}{}^{I}$-field plays the role of a Stueckelberg compensator absorbed into the longitudinal component of $B_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I}$. We give not only the component Lagrangian, but also a corresponding superspace reformulation, reconfirming the total consistency of the system. The adjoint representation of the TM and CVM is further generalized to an arbitrary real representation of general $SO(N)$ gauge group. We also couple the globally $N=1$ supersymmetric system to supergravity, as an additional nontrivial confirmation.