Constrained superfields from an anti-D3-brane in KKLT

The KKLT construction of dS vacua relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this anti-D3-brane is an excited state in a supersymmetric theory since it can decay to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry spontaneously and one should be able to package all the world-volume fields on the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3-brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy $S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming publication) that the vector field $A_\mu$ and the three scalars $\phi^i$ give rise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$ that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \bar H^i)=0$. This is the first time that such constrained multiplets appear in string theory constructions.