Twisted indices of 3d $$ \mathcal{N} $$ = 4 gauge theories and enumerative geometry of quasi-maps
Twisted indices of 3d $$ \mathcal{N} $$ = 4 gauge theories and enumerative geometry of quasi-maps
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3d $$ mathcal{N} $$ 的扭曲索引 = 4 个规范理论和准映射的枚举几何
DOI：
10.1007/jhep07(2019)014
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发表时间：
2019
影响因子：
5.4
通讯作者：
Bullimore M
中科院分区：
文献类型：
--
作者：
Bullimore M
我们探讨了S 1x Σ上三维= 4规范理论的扭曲指数的几何解释，其中Σ是一个封闭的黎曼曲面。我们集中讨论了一类在一般质量和FI参数变形下具有孤立真空的超对称颤振规范理论。我们证明了路径积分局部化到Σ上广义涡旋方程解的模空间，它可以被代数地理解为到希格斯分支的准映射。我们证明了扭曲指标再现了扭曲拟映射模空间的虚欧拉特征，并证明了这与先前工作中引入的轮廓积分表示一致。最后，我们在此背景下研究了三维= 4镜像对称性，这意味着在交换等变和计数参数的情况下，与希格斯分支镜像对相关的枚举不变量是相等的。
We explore the geometric interpretation of the twisted index of 3d= 4 gauge theories on S 1× Σ where Σ is a closed Riemann surface. We focus on a rich class of supersymmetric quiver gauge theories that have isolated vacua under generic mass and FI parameter deformations. We show that the path integral localises to a moduli space of solutions to generalised vortex equations on Σ, which can be understood algebraically as quasi-maps to the Higgs branch. We show that the twisted index reproduces the virtual Euler characteristic of the moduli spaces of twisted quasi-maps and demonstrate that this agrees with the contour integral representation introduced in previous work. Finally, we investigate 3d= 4 mirror symmetry in this context, which implies an equality of enumerative invariants associated to mirror pairs of Higgs branches under the exchange of equivariant and degree counting parameters.