On the existence of scaling multi-centered black holes
arXiv:2110.06652 · doi:10.1007/s00023-022-01185-x
Abstract
For suitable charges of the constituents, the phase space of multi-centered BPS black holes in N=2 four-dimensional supergravity famously exhibits scaling regions where the distances between the centers can be made arbitrarily small, so that the bound state becomes indistinguishable from a single-centered black hole. In this note we establish necessary conditions on the Dirac product of charges for the existence of such regions for any number of centers, generalizing the standard triangular inequalities in the three-center case. Interestingly, the same conditions are necessary for the existence of multi-centered solutions at the attractor point. We prove that similar conditions are also necessary for the existence of self-stable representations of the corresponding quiver, as suggested by the duality between the Coulomb and Higgs branches of supersymmetric quantum mechanics.
arXiv commentIn this v3 we have changed a bit the presentation according to our reviewer's suggestions, and have extended the results on the Higgs branch to a wider generality
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