  We solve for the complete space of linearized deformations of the
Klebanov-Strassler background consistent with the symmetries preserved by a
stack of anti-D3 branes smeared on the $S^3$ of the deformed conifold. We find
that the only solution whose UV physics is consistent with that of a
perturbation produced by anti-D3 branes must have a singularity in the
infrared, coming from NS and RR three-form field strengths whose energy density
diverges. If this singularity is admissible, our solution describes the
backreaction of the anti-D3 branes, and is thus likely to be dual to the
conjectured metastable vacuum in the Klebanov-Strassler field theory. If this
singularity is not admissible, then our analysis strongly suggests that anti-D3
branes do not give rise to metastable Klebanov-Strassler vacua, which would
have dramatic consequences for some string theory constructions of de Sitter
space. Key to this result is a simple, universal form for the force on a probe
D3-brane in our ansatz.
