Supersymmetric anti-D3-brane action in the Kachru-Kallosh-Linde-Trivedi setup

An anti-D3-brane plays a crucial role in the construction of semirealistic cosmological models in string theory. Part of its action provides an uplift term that has been used to lift anti-de Sitter solutions to phenomenologically viable de Sitter vacua in the Kachru-Kallosh-Linde-Trivedi and large volume scenario (LVS) setups. In the last few years it has been shown that this uplift breaks supersymmetry spontaneously and can be described in the four-dimensional N=1 supergravity language by using constrained supermultiplets. Here we derive the complete four-dimensional N=1 supergravity action for an anti-D3-brane coupled to all closed-string background fields. In particular, we include the vector field, the scalar fields, and all fermions that live on the anti-D3-brane.