Multi-center black hole saddles for the supersymmetric index exist at finite temperature, their on-shell action is the sum of extremal entropies, and the entire moduli space of saddles vanishes at walls of marginal stability.
On Israel-Wilson-Perjes black holes
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We show, under certain conditions, that regular Israel-Wilson-Perj\'es black holes necessarily belong to the Majumdar-Papapetrou family.
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Multicentered black hole saddles for supersymmetric indices
Multi-center black hole saddles for the supersymmetric index exist at finite temperature, their on-shell action is the sum of extremal entropies, and the entire moduli space of saddles vanishes at walls of marginal stability.