Constrained superfields from an anti-D3-brane in KKLT

The KKLT construction of dS vacua [1] relies on an uplift term that arises from an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde [2] that this anti-D3brane 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 A1 = 1 supersymmetric action. Here we extend previous results and identify the constrained superfields that correspond to all the degrees of freedom on the anti-D3brane. In particular, we show explicitly that the four 4D worldvolume spinors give rise to constrained chiral multiplets S and Y-i = 1, 2, 3 that satisfy S-2 = SYi = 0. We also conjecture (and provide evidence in a forthcoming publication) that the vector field Ap and the three scalars 0' give rise to a field strength multiplet W-alpha and three chiral multiplets Hi that satisfy the constraints SW alpha = (D) over bar(alpha) over dot (S (II) over bar (i)) = 0. This is the first time that such constrained multiplets appear in string theory constructions.