论文标题
拓扑相关因子和表面缺陷来自同类的同胞
Topological Correlators and Surface Defects from Equivariant Cohomology
论文作者
论文摘要
我们在三维流形的一般类别上找到了$ \ Mathcal {n} = 4 $ Matter Theyes的一维保护子部门。通过模棱两可的定位，我们在三个维度上确定了原始模型的双量子力学计算BPS相关器。具体而言，将Atiyah-Bott-Berline-vergne公式应用于原始动作表明，这本地化在一维动作上，并在适当的异构体的定点子手机上支撑。我们首先表明我们的方法复制了以$ s^3 $获得的先前结果。然后，我们将其应用于$ s^2 \ times s^1 $的新颖情况，并表明该理论本地化在两个非相互作用的量子力学上，并具有不相交的支持。我们证明，此类模型的BPS运算符自然与非交通性星级产品相关，而其相关功能本质上是拓扑的。最后，我们将三维理论与一般$ \ MATHCAL {n} =（2,2）$表面缺陷相结合，并扩展了本地化计算以捕获混合维度系统的完整分区功能和BPS相关器。
We find a one-dimensional protected subsector of $\mathcal{N}=4$ matter theories on a general class of three-dimensional manifolds. By means of equivariant localization, we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on $S^3$. Then, we apply it to the novel case of $S^2 \times S^1$ and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncommutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $\mathcal{N}=(2,2)$ surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.
