A supersymmetric spin current

TL;DR

This paper explores the supersymmetric structure of spin currents in four-dimensional $ =1$ theories, revealing a duality that links the spin current to the stress tensor multiplet and suggesting holographic applications involving background torsion.

Contribution

It identifies the spin current with the Hodge dual of the stress tensor multiplet's bottom component in supersymmetric theories, extending understanding of spin currents in holography.

Findings

Spin current is dual to the stress tensor multiplet's bottom component.

Holographic theories may use the Hodge dual of the R current as a spin current.

Framework applies broadly to $ =1$ supersymmetric theories.

Abstract

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.