论文标题
颤抖的渐近学和变形虫：卡拉比伊au三倍的曲折的激发
Quiver Asymptotics and Amoeba: Instantons on Toric Divisors of Calabi-Yau Threefolds
论文作者
论文摘要
先前使用二维晶体熔化模型和二聚体模型研究了Calabi-yau三倍的非紧密分隔的D4-D2-D0 Brane的BPS结合状态和双箭筒理论中的激体状态。使用与感谢您的颤动相关的热带几何形状，我们研究了颤抖仪理论的渐近学来计算其一些热力学可观察物并提取相结构。我们得到的是，从晶体模型的极限形状，变形虫的边界及其harnack曲线表征从极限形状明确获得热力学可观察物，例如自由能，熵和生长速率。此外，我们观察到，从晶体模型中波动的牙龈分布中推断出的instanton扇区中存在Hagedorn相变。我们在一些$ \ Mathbb {C}^3 $的具体示例中介绍了结果的明确计算，Conifold，Local $ \ Mathbb {p}^1 \ times \ times \ times \ Mathbb {p}^1 $和local $ \ Mathbb {p}^2 $ quivers。
The BPS bound states of D4-D2-D0 branes on the non-compact divisors of Calabi-Yau threefolds and the instantons in the dual quiver gauge theories are previously studied using two-dimensional crystal melting model and dimer model. Using the tropical geometry associated with the toric quiver, we study the asymptotic of the quiver gauge theory to compute some of their thermodynamic observables and extract the phase structure. We obtain that the thermodynamic observables such as free energy, entropy and growth rate are explicitly obtained from the limit shape of the crystal model, the boundary of the Amoeba and its Harnack curve characterization. Furthermore, we observe that there is a Hagedorn phase transition in the instanton sector inferred from the Gumbel distribution of the fluctuations in the crystal model. We present explicit computations of the results in some concrete examples of $\mathbb{C}^3$, conifold, local $\mathbb{P}^1\times \mathbb{P}^1$ and local $\mathbb{P}^2$ quivers.
