Constructing the Supersymmetric anti-D3-brane action in KKLT

The derivation of the complete anti-D3-brane low energy effective action in KKLT is reviewed. All worldvolume fields are included, together with the background moduli. The result is recast into a manifest supersymmetric form in terms of the three independent functions of $\mathcal{N}=1$ supergravity in four dimensions: the Kaehler potential, the superpotential and the gauge kinetic function. The latter differs from the expression one would expect by analogy with the D3-brane case.