Anti-brane singularities as red herrings

Unphysical 3-form flux singularities near anti-branes have been argued to get resolved in the classical supergravity regime when brane polarisation is properly taken into account. The only example that does not seem to fit this logic is the $\bar{\text{D6}}$-brane because of a no-go theorem for well behaved supergravity solutions with negative D6 charge. In this paper we first review the existing results demonstrating how brane polarisation resolves singularities for $\bar{\text{D3}}$-branes and then we improve on the description of the polarisation of $\bar{\text{D6}}$-branes into KK5 dipoles. We argue that the meta-stable state carries exactly zero (anti-)D6 charge, which is the unique way around the no-go theorem. We then provide numerical evidence for well-behaved solutions that describe such meta-stable states.