Speaker
Boris Pioline, Jussieu
Abstract
The BPS spectrum in type IIA strings compactified on a Calabi-Yau threefold $X$ depends sensitively on K\”ahler moduli, with a dense set of walls separating chambers where the BPS index is constant. The Attractor Flow Tree Formula gives a way to decompose the spectrum into bound states of elementary constituents which no longer depend on Kahler moduli. When $X$ is the resolution of a toric CY singularity, the BPS spectrum of the corresponding 5D gauge theory can be described near the singularity by a quiver, but this description breaks down at finite volume. Scattering diagrams provide the natural mathematical framework for the Attractor Flow Tree Formula, and give a global description of the BPS spectrum interpolating between orbifold points and large volume. I will construct the scattering diagram for the simplest del Pezzo surfaces, namely the local projective space $K_{P^2}$ and local Hirzebruch surface $K_{P^1\times P^1]$, thereby completely characterizing the BPS spectrum in these examples. Based on [arXiv:2210.10712] in collaboration with Pierrick Bousseau, Pierre Descombes and Bruno Le Floch, and work to appear with Bruno and my student Rishi Raj.