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Attractor flow trees and scattering diagrams

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BLHW01 - Number theory, machine learning and quantum black holes

In string models with N=2 supersymmetry in 4 dimensions, the Split Attractor Flow Tree Conjecture (SAFT) posits that the BPS index $\Omega_z(\gamma)$ for given charge $\gamma$ and moduli z can be computed from the so-called attractor indices, counting BPS states in their respective attractor chamber, by summing over a finite set of binary trees known as attractor flow trees. The goal of this work is to demonstrate the SAFT for type IIA string theory reduced on local P^2, one of the simplest non-compact Calabi-Yau threefolds, for which attractor indices are completely known. Mathematically, this amounts to constructing the stability scattering diagram in the space of Bridgeland stability conditions. Based on [arXiv:2210.10712] in collaboration with Pierrick Bousseau, Pierre Descombes and Bruno Le Floch.

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