论文标题
指数BPS图和D-Brane在曲曲曲曲曲bi-yau上计数三倍：第二部分
Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II
论文作者
论文摘要
我们在$ s^1 \ times \ mathbb {r}^4 $上研究5D $ \ MATHCAL {n} = 1 $ $ su（2）$ $ su（2）$ $ su（2）$ $ su（2）$ yang-mills理论的BPS状态。几何工程将它们与本地Hirzebruch Surface $ \ Mathbb {F} _0 $的列举不变性有关。我们通过指数网络说明了VAFA字体不变的计算，并在模量空间中某些点验证频谱的纤维碱基对称性，并与基于颤音和特殊集合的镜像描述匹配。尽管是无限的，但频谱的一部分是由简单代数方程描述的家庭中组织的。改变M理论圆的半径与4D $ \ MATHCAL {n} = 2 $ Seiberg-Witten理论的光谱平滑地插值，从而恢复了极限的光谱网络。
We study BPS states of 5d $\mathcal{N}=1$ $SU(2)$ Yang-Mills theory on $S^1\times \mathbb{R}^4$. Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface $\mathbb{F}_0$. We illustrate computations of Vafa-Witten invariants via exponential networks, verifying fiber-base symmetry of the spectrum at certain points in moduli space, and matching with mirror descriptions based on quivers and exceptional collections. Albeit infinite, parts of the spectrum organize in families described by simple algebraic equations. Varying the radius of the M-theory circle interpolates smoothly with the spectrum of 4d $\mathcal{N}=2$ Seiberg-Witten theory, recovering spectral networks in the limit.
