In this summer, i learnt about various muliplet in Supergravity. First i summarize what i learn from the school.
(i) Ferrar-Zumino multiplet
The super-current multiplet satisfies \begin{align} \bar{D}^{\dot{\alpha}}J_{\alpha \dot{\alpha}} = D_\alpha \Phi \end{align} where $\Phi$ is chiral superfield.
This multiplet couples to old-minimal supergravity which has redundant $6=4+2$ degrees of freedom of bosonic variable.
(ii) R - multiplet
The super-current multiplet satisfies \begin{align} \bar{D}^{\dot{\alpha}}J_{\alpha \dot{\alpha}} = W_\alpha \end{align} with \begin{align} \bar{D}_{\dot{\beta}} W_\alpha = D^\alpha W_\alpha = \bar{D}^{\dot{\alpha}} \bar{W}_{\dot{\alpha}}=0 \end{align}
This multiplet couples to new-minimal supergravity which has redudant $6=3+3$ degrees of freedom of bosonic variable.
(And the lecture says it is related with $R$-symmetry. How?)
(iii) S-multiplet
The super-current multiplet satisfies \begin{align} \bar{D}^{\dot{\alpha}}J_{\alpha \dot{\alpha}} = D_\alpha \Phi + W_\alpha \end{align} where $\Phi$ is chiral superfield.
It has $(16,16)$ multiplet. The name $S$ is something to do with Seiberg.
And it couples to non-minimal supergravity models.
(Is the $S$ relateds with Seiberg duality?, )
Can anyone can explain detail about meaning of super-current equation for each multiplet, and if possible various viewpoint of these supergravity multiplet? (bolded parts are also my question arise from the school)