A comment on anti-brane singularities in warped throats

We compute the imaginary self-dual (ISD) and imaginary anti-self-dual (IASD) fluxes for the Klebanov-Strassler background perturbed by a stack of p anti-D3 branes. We show that, at linear order in p, they both have a singularity in the near-brane region. While one can argue that the IASD flux may disappear at full non-linear level, no such argument exists for the ISD mode. An analogy with anti-D6 backreaction suggests that such singularity may survive once full backreaction is taken into account and may be a universal feature of anti-brane solutions.