Soft branes in supersymmetry-breaking backgrounds

We revisit the analysis of effective field theories resulting from non-supersymmetric perturbations to supersymmetric flux compactifications of the type-IIB superstring with an eye towards those resulting from the backreaction of a small number of anti-D3-branes. Independently of the background, we show that the low-energy Lagrangian describing the fluctuations of a stack of probe D3-branes exhibits soft supersymmetry breaking, despite perturbations to marginal operators that were not fully considered in some previous treatments. We take this as an indication that the breaking of supersymmetry by anti-D3-branes or other sources may be spontaneous rather than explicit. In support of this, we consider the action of an anti-D3-brane probing an otherwise supersymmetric configuration and identify a candidate for the corresponding goldstino.