Branes, Bundles and Attractors: Bogomolov and Beyond

D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck

In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya $C^{\infty}$-manifolds with a fundamental module and morphisms therefrom to a complex manifold. In the current sequel, we use this notion to give a prototypical definition of supersymmetric D-branes of A-type (i.e. A-branes) -- in an appropriate region of the Wilson's theory-space of string theory -- as special Lagrangian morphisms from such objects with a unitary, minimally flat connection-with-singularities. This merges Donaldson's picture of special Lagrangian submanifolds and the Polchinski-Grothendieck Ansatz …

吸引子不变量、膜砖与晶体

Attractor invariants, brane tilings and crystals

本文研究环面卡拉比-丘三维流形上的吸引子 DT 不变量，利用膜砖与带势箭图方法进行显式计算，预测了所有吸引子不变量的值，并验证其与熔融晶体计数的一致性。

Wall-crossing of D4-D2-D0 and flop of the conifold

We discuss the wall-crossing of the BPS bound states of a non-compact holomorphic D4-brane with D2 and D0-branes on the conifold. We use the Kontsevich-Soibelman wall-crossing formula and analyze the BPS degeneracy in various chambers. In particular we obtain a relation between BPS degeneracies in two limiting attractor chambers related by a flop transition. Our result is consistent with known results and predicts BPS degeneracies in all chambers.

局部 $P^2$ 上的 BPS 树木学

BPS Dendroscopy on Local $P^2$

本文结合大体积与 orbifold 点附近的散射图结果，证明在非紧 Calabi–Yau 三维流形 $K_{P^2}$ 的 $Π$-稳定性物理切片上，Split Attractor Flow Conjecture 成立。