Interacting Vector-Spinor and Nilpotent Supersymmetry

Abstract

We formulate an interacting theory of a vector-spinor field that gauges anticommuting spinor charges \{Q_α^I, Q_β^J \} = 0 in arbitrary space-time dimensions. The field content of the system is (ψ_μ^{αI}, χ^{αI J}, A_μ^I), where ψ_μ^{αI} is a vector-spinor in the adjoint representation of an arbitrary gauge group, and A_μ^I is its gauge field, while χ^{αI 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.