Abstract
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.
Highlights
We argue that the meta-stable state carries exactly zeroD6 charge, which is the unique way around the no-go theorem
We have argued that the no-go theorems against the existence of backreacted solutions with regular H3-flux are evaded in a peculiar way predicted by our probe computation because the polarised state has exactly zero anti-brane charge
In the same figure we show the flux-clumping of H3, which in the BPS solution would be identically 1 for all r, but here we can see that the flux has clumped around r = 0 and drained from the UV, and has a regular profile. We find that this solution is consistent with the expectations of a non-BPS solution corresponding to the supergravity solution of a polarised D6-brane remnant at r = 0, and that it is numerically reliable
Summary
Is not a valid description at small string coupling and neither is the non-Abelian D3 action that was used in the same paper This is not particular to D3’s but applies to all situations including M2-brane meta-stable states [9]. Instead the computations carried out in [31,33] are applicable in the supergravity regime and showed that the singularities were an artefact of using a too restrictive supergravity Ansatz; in short the Ansatz did not include the polarised brane, which is predicted to be there from the probe analysis This was already suggested earlier by Dymarsky in [34] (see [35, 36] for related comments). The reason is surprisingly simple; the meta-stable probes polarise rather strongly until they reach exactly the point where the monopole D6-brane charge vanishes. The Ansatz should be rich enough to allow for the NS5-brane, predicted in the probe analysis, to appear and backreact on the geometry
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