论文标题
晶体融化，BPS颤抖和杂质
Crystal Melting, BPS Quivers and Plethystics
论文作者
论文摘要
我们研究了所有曲奇的calabi-yau三倍，没有紧凑的4循环和一些非态例的D6-D2-D0 Brane结合状态D6-D2-D0 Brane结合状态的精制和未精制的晶体/BPS分区。它们可以写为（广义）MacMahon功能的产品。我们检查表达式并将其用作真空字符来研究粘合物。然后，我们考虑墙壁交叉点，并讨论不同腔室的可能的晶体描述。我们还根据多个指数表达了分区功能。对于$ \ mathbb {c}^3 $和三倍的仿射式颤抖，我们找到了它们与nilpotent kac多项式的连接。同样，可以通过用（概括）欧拉函数倒数替换（广义的）MacMahon函数来获得D4-D2-D0 Brane结合状态的分区函数。
We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized) MacMahon functions. We check our expressions and use them as vacuum characters to study the gluings. We then consider the wall crossings and discuss possible crystal descriptions for different chambers. We also express the partition functions in terms of plethystic exponentials. For $\mathbb{C}^3$ and tripled affine quivers, we find their connections to nilpotent Kac polynomials. Similarly, the partition functions of D4-D2-D0 brane bound states can be obtained by replacing the (generalized) MacMahon functions with the inverse of (generalized) Euler functions.
