Observations on fluxes near anti-branes

We revisit necessary conditions for gluing local (anti-)D3 throats into flux throats with opposite charge. These consistency conditions typically reveal singularities in the 3-form fluxes whose meaning is being debated. In this note we prove, under well-motivated assumptions, that unphysical singularities can potentially be avoided when the anti-branes polarise into spherical NS5 branes, with a specific radius. If a consistent solution can then indeed be found, our analysis seems to suggests a rather large correction to the radius of the polarization sphere compared to the probe result. We furthermore comment on the gluing conditions at finite temperature and point out that one specific assumption of a recent no-go theorem can be broken if anti-branes are indeed to polarise into spherical NS5 branes at zero temperature.