Interacting Vector-Spinor and Nilpotent Supersymmetry

We formulate an interacting theory of a vector-spinor field that gauges anticommuting spinor charges \{Q_\alpha{}^I, Q_\beta{}^J \} = 0 in arbitrary space-time dimensions. The field content of the system is (\psi_\mu{}^{\alpha I}, \chi^{\alpha I J}, A_\mu{}^I), where \psi_\mu{}^{\alpha I} is a vector-spinor in the adjoint representation of an arbitrary gauge group, and A_\mu{}^I is its gauge field, while \chi^{\alpha I J} is an extra spinor with antisymmetric adjoint indices I J. Amazingly, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions.