论文标题
3D ADHM QUIVER仪表中的块和涡流理论
Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
论文作者
论文摘要
我们研究了三维$ \ Mathcal {n} = 4 $ supersymmetric $ u（n）$仪表理论的半球分区函数，具有一个伴随，一个基本的超级超级超值 - ADHM QUIVER理论。特别是，我们提出了一组杰出的紫外线条件，该条件产生了希格斯和库仑分支的定量手性环的Verma模块。根据两位作者与Bullimore合作的最新提案，我们明确地表明，半球分区功能在两个限制中恢复了这些模块的特征，并实现了块准确地粘贴在封闭的三个manifolds上的理论函数的块。我们研究了涡流模量空间的几何形状，并研究了涡流分区的解释，作为准积分的质量指数与$ \ mathbb {c}^2 $中的Hilbert方案的等效指数。我们还研究了在线路运算符的存在下，ADHM颤抖仪理论的一半索引，并讨论其几何解释。在途中，我们发现半球块与拓扑弦理论和等效量子K理论之间的有趣关系。
We study the hemisphere partition function of a three-dimensional $\mathcal{N}=4$ supersymmetric $U(N)$ gauge theory with one adjoint and one fundamental hypermultiplet -- the ADHM quiver theory. In particular, we propose a distinguished set of UV boundary conditions which yield Verma modules of the quantised chiral rings of the Higgs and Coulomb branches. In line with a recent proposal by two of the authors in collaboration with M. Bullimore, we show explicitly that the hemisphere partition functions recover the characters of these modules in two limits, and realise blocks gluing exactly to the partition functions of the theory on closed three-manifolds. We study the geometry of the vortex moduli space and investigate the interpretation of the vortex partition functions as equivariant indices of quasimaps to the Hilbert scheme of points in $\mathbb{C}^2$. We also investigate half indices of the ADHM quiver gauge theory in the presence of a line operator and discuss their geometric interpretation. Along the way we find interesting relations between our hemisphere blocks and related quantities in topological string theory and equivariant quantum K-theory.
