Anti-D3's - Singular to the Bitter End
Iosif Bena, Mariana Grana, Stanislav Kuperstein, Stefano Massai

TL;DR
This paper analyzes the backreaction of smeared anti-D3 branes on the deformed conifold, showing that regular solutions must be anti-Klebanov-Strassler and negative IR D3-charge solutions are not possible.
Contribution
It provides a power counting argument demonstrating the necessity of imaginary-anti-self-dual fluxes for regular anti-D3 brane solutions on the conifold.
Findings
Only the anti-Klebanov-Strassler solution is regular in IR and UV.
Solutions with negative IR D3-charge and positive UV D3-charge are not regular.
Regular solutions require IR fluxes to be imaginary-anti-self-dual.
Abstract
We study the full backreaction of anti-D3 branes smeared over the tip of the deformed conifold. Requiring the 5-form flux and warp factor at the tip to be that of anti-D3 branes, we find a simple power counting argument showing that if the three-form fluxes have no IR singularity, they will be necessarily imaginary-anti-self-dual. Hence the only solution with anti-D3 branes at the tip of the conifold that is regular in the IR and the UV is the anti-Klebanov-Strassler solution, and there is no regular solution whose D3-charge is negative in the IR and positive in the UV.
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