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The KKLT construction of dS vacua relies on an uplift term that arises froman anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that thisanti-D3-brane is an excited state in a supersymmetric theory since it can decayto a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetryspontaneously and one should be able to package all the world-volume fields onthe anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action.Here we extend previous results and identify the constrained superfields thatcorrespond to all the degrees of freedom on the anti-D3-brane. In particular,we show explicitly that the four 4D worldvolume spinors give rise toconstrained 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 forthcomingpublication) that the vector field $A_\mu$ and the three scalars $\phi^i$ giverise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \barH^i)=0$. This is the first time that such constrained multiplets appear instring theory constructions.

Constrained superfields from an anti-D3-brane in KKLT