String Theory Origin of Constrained Multiplets

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector $A_μ$, three complex scalars $ϕ^i$ and four 4d fermions $λ^0$, $λ^i$. These transform, in addition to the more familiar N=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear N=1 multiplets: four chiral multiplets $S$, $Y^i$ that satisfy $S^2=SY^i=0$ and contain the worldvolume fermions $λ^0$ and $λ^i$; and four chiral multiplets $W_α$, $H^i$ that satisfy $S W_α=0$ and $S \bar D_{\dot α} \bar H^{\bar \imath}=0$ and contain the vector $A_μ$ and the scalars $ϕ^i$. We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet $Φ$ that satisfies $S(Φ-\bar Φ)=0$, which is particularly interesting for inflationary cosmology.

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