来自 Jeffrey-Kirwan 留数的晶体与双重箭图代数

四维Pandharipande-Thomas顶点与Jeffrey-Kirwan残差

The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue

本文提出一种轮廓积分方法计算四维K理论equivariant Pandharipande-Thomas顶点，并展示通过选择不同参考向量可将该顶点与Donaldson-Thomas顶点关联。通过曲线和曲面示例，探讨了四维设定下的DT/PT对应关系及其高阶和超群推广。

Amplituhedron meets Jeffrey-Kirwan Residue

The tree amplituhedra $\mathcal{A}_{n,k}^{(m)}$ are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for $m=4$ as a geometric construction encoding tree-level scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, they are mathematically interesting for any $m$. In this paper we strengthen the relation between scattering amplitudes and geometry by linking the amplituhedron to the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry. We focus on a particular class of amplituhedra in any dimension, namely cycli…

On the Jeffrey-Kirwan residue of BCD-instantons

We apply the Jeffrey-Kirwan method to compute the multiple integrals for the $BCD$ type Nekrasov partition functions of four dimensional $\mathcal{N}=2$ supersymmetric gauge theories. We construct a graphical distinction rule to determine which poles are surrounded by their integration cycles. We compute the instanton correction of the "$Sp(0)$" pure super-Yang-Mills theory and find that $Z^{Sp(0)}_{k}=(-1)^{k}(2^{k}k!\varepsilon_{1}^{k}\varepsilon_{2}^{k})^{-1}$ for $k\le 8$, which resembles the formula $Z^{U(1)}_{k}=(k!\varepsilon_{1}^{k}\varepsilon_{2}^{k})^{-1}$ for the pure super-Yang-Mil…

对数 Calabi–Yau 曲面与 Jeffrey–Kirwan 残数

Log Calabi-Yau surfaces and Jeffrey-Kirwan residues

本文证明无环无有向圈箭图相关亚纯形式的 Jeffrey–Kirwan 残数等于其 Donaldson–Thomas 型不变量，并在完全二部箭图情形借助散射图与 theta 函数说明其由 Gross–Hacking–Keel 镜像族确定。

Quiver indices and Abelianization from Jeffrey-Kirwan residues

In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stable quiver representations. Using supersymmetric localization, the refined Witten index can be expressed as a residue integral with a specific contour prescription, originally due to Jeffrey and Kirwan, depending on the stability parameters. On the other hand, the physical picture of quiver quantum mechanics describing interactions of BPS black holes predicts that the refined Witten index of a non-Abelian quiver c…

BPS态计数中Calabi-Yau晶体的起源

The Origin of Calabi-Yau Crystals in BPS States Counting

本文研究一般环面Calabi-Yau流形上BPS D-膜计数，通过计算味Witten指数的Jeffrey-Kirwan留数，发现BPS简并度由晶体熔化模型描述；三维情形重现已知模型，四维情形需赋予晶体构型非平凡权重，并将三维与四维统一处理。