We study the effective field theory of KKLT and LVS moduli stabilisation
scenarios coupled to an anti-D3-brane at the tip of a warped throat. We
describe the presence of the anti-brane in terms of a nilpotent goldstino
superfield in a supersymmetric effective field theory. The introduction of this
superfield produces a term that can lead to a de Sitter minimum. We fix the
Kaehler moduli dependence of the nilpotent field couplings by matching this
term with the anti-D3-brane uplifting contribution. The main result of this
paper is the computation, within this EFT, of the soft supersymmetry breaking
terms in both KKLT and LVS for matter living on D3-brane (leaving the D7-brane
analysis to an appendix). A handful of distinct phenomenological scenarios
emerge that could have low energy implications, most of them having a split
spectrum of soft masses. Some cosmological and phenomenological properties of
these models are discussed. We also check that the attraction between the
D3-brane and the anti-D3-brane does not affect the leading contribution to the
soft masses and does not destabilise the system.Comment: 26+14 pages, 1 figure; references and clarifications added, typos
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