10.03.2021 (Wednesday)

Attractor indices, brane tilings and crystals

Regular Seminar Boris Pioline (LPTHE Jussieu)

14:00 IC
room Zoom -- instructions in abstract

In type II strings compactified on a Calabi-Yau threefold $X$, the Donaldson-Thomas (DT) invariants $\Omega(\gamma,z)$ counting BPS black holes have an intricate dependence on the moduli $z$, due to wall-crossing phenomena. When $X$ is a toric threefold, these indices are related to the DT invariants of a quiver with potential with superpotential, encoded by a brane tiling. I will present a conjecture for the DT invariants for all dimension vectors $d$ in a certain chamber $z_*(d)$ known as the attractor (or self-stability) chamber. In short, "DT invariants all vanish, except when they are known not to." In combination with the attractor flow tree formulae, this conjecture provides an algorithmic way of computing the DT invariants $\Omega(\gamma,z)$ for any $\gamma,z$. The conjecture is supported by a large number of checks, including a successful comparison with the Vafa-Witten invariants of a Fano surface $S$ when $X$ is the total space of the canonical bundle $K_S$, and with the counting of molten crystals for framed DT invariants in the non-commutative chamber. Based on works with G. Beaujard, J. Manschot and S. Mozgovoy, arXiv:2004.14466 and 2012.14358 Join Zoom Meeting https://zoom.us/j/94029175955?pwd=b1hvVnVxbFZjTmM5bkxaWi93VkpzUT09 Meeting ID: 940 2917 5955 Passcode: 086150