Anti-D3's - Singular to the Bitter End

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.