BPS black holes, wall-crossing and mock modularity of higher depth
Résumé
A class of BPS solutions in N=2 supergravity describes multi-centered black holes. Generically, they are stable only in a chamber of the moduli space so that the BPS index, counting these solutions, jumps across walls of marginal stability. I'll show how the attractor flow conjecture allows to express this index in terms of "attractor degeneracies" counting black holes at the
attractor point. Besides, using duality constraints from string theory, I predict the behavior of the generating function of these degeneracies under modular transformations, which connects it to the theory of mock modular forms.