String theory origin of constrained multiplets

Abstract

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 $$ \mathcal{N}=4 $$ 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 $$ \mathcal{N}=1 $$ 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 $$ S{W}_{\alpha }=S{\overline{D}}_{\overset{\cdotp }{\alpha }}{\overline{H}}^{\overline{\imath}}=0 $$ 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 $$ S\left(\Phi -\overline{\Phi}\right)=0 $$ , which is particularly interesting for inflationary cosmology.