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-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 $$ mathcal{n} $$ = 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 μ and the three scalars ϕ i give rise to a field strength multiplet w α and three chiral multiplets h i that satisfy the constraints $$ s{w}_{alpha }={overline{d}}_{overset{cdot }{alpha }}left(s{overline{h}}^iright)=0 $$ . this is the first time that such constrained multiplets appear in string theory constructions.