有理分支的有向图规范理论与对称化

Branches, quivers, and ideals for knot complements

We generalize the $F_K$ invariant, i.e. $\widehat{Z}$ for the complement of a knot $K$ in the 3-sphere, the knots-quivers correspondence, and $A$-polynomials of knots, and find several interconnections between them. We associate an $F_K$ invariant to any branch of the $A$-polynomial of $K$ and we work out explicit expressions for several simple knots. We show that these $F_K$ invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using $R$-matrices. We …

通过拟映射的量子引田猜想

The quantum Hikita conjecture via quasimaps

本文提出细化的量子引田猜想并建立通用证明框架，对两类规范理论完成证明，还利用量子引田同构给出量子库仑分支分次迹的几何描述。

库仑分支、量子化 zastavas、卡茨多项式与洗牌代数

Coulomb branches, quantized zastavas, Kac polynomials, and shuffle algebras

研究利用基本单极子算子构造卡茨 - 穆迪仿射格拉斯曼切片闭嵌入，通过特定 BFN 构造变体实现量子化，进而构造极限量子化 zastava 及其正部，证明其希尔伯特级数与卡茨多项式相关，还证明了内古特猜想。

Coulomb 分支的函子性

Functoriality of Coulomb branches

本文证明了GL_n或SL_n抛物基仿射空间余切丛的仿射闭包是Coulomb分支，证实了相关猜想。核心方法是通过引入可粘接假设，利用特定的Hamilton约化过程建立Coulomb分支的函子性，并指出任何无环箭图的Coulomb分支均可由两顶点箭图获得。

量子化库仑分支的残差构造

Residue construction of quantized Coulomb branches

该研究描述了量子化BFN库仑分支在局域化映射下的像，给出了类似DAHA构造的根与残差条件，并为量子化锥形库仑分支提供了球迹的数学构造。

关于3维N=4规范理论暂定Coulomb分支的问题

Questions on provisional Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories

本文探讨3维N=4超对称规范理论暂定Coulomb分支的性质，结合Higgs分支及级数秩对偶性，通过实例分析其数学结构。

A Family of ${\rm GL}_r$ Multiplicative Higgs Bundles on Rational Base

In this paper we study a restricted family of holomorphic symplectic leaves in the Poisson-Lie group ${\rm GL}_r(\mathcal{K}_{\mathbb{P}^1_x})$ with rational quadratic Sklyanin brackets induced by a one-form with a single quadratic pole at $\infty \in \mathbb{P}_{1}$. The restriction of the family is that the matrix elements in the defining representation are linear functions of $x$. We study how the symplectic leaves in this family are obtained by the fusion of certain fundamental symplectic leaves. These symplectic leaves arise as minimal examples of (i) moduli spaces of multiplicative Higgs…

Nonabelian Mirror Symmetry Beyond the Chiral Ring

Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications for understanding nonperturbative physics in general 3D quantum field theories. We study mirror symmetry in 3D $\mathcal{N}=4$ supersymmetric field theories whose Higgs or Coulomb branches realize $D$- and $E$-type Kleinian singularities in the $ADE$ classification, generalizing previous work on the $A$-type case. Such theories include the $SU(2)$ gauge theo…

非共轭型的库仑分支：物理学视角

Coulomb Branches of Noncotangent Type: a Physics Perspective

从物理学角度研究非共轭型3D $\mathcal{N}=4$ 理论的库仑分支，通过扩展半球分区函数方法，推导库仑分支算符代数并分析其结构。