A supersymmetric spin current

We study the supersymmetric structure of the spin current in four dimensional $\mathcal{N}=1$ supersymmetric theories. By coupling the stress tensor multiplet to a vierbein multiplet we identify a spin current with the Hodge dual of the bottom component of the stress tensor multiplet in a wide range of theories. This implies that in holographic theories the Hodge dual of the $R$ current may serve as a spin current, paving the way for holographic studies of theories with background torsion.