标题： 全局变体的$\mathcal{N}=1^*$理论与 Calogero-Moser 系统 显示英文标题

标题： Global variants of $\mathcal{N}=1^*$ theories and Calogero-Moser systems

摘要： 四维规范理论的全局变体由其真实的威尔逊-‘t Hooft线算符的谱来指定。 当时空被取为 $\mathbb{R}^3 \times S^1$时，变体的选择具有重要意义。 我们专注于与扭曲椭圆Calogero-Moser系统密切相关的 $\mathcal N=1^*$理论。 一般性地，我们通过引入李代数相关的复多体可积系统的全局变体概念，阐明了这种规范理论拓扑数据如何在可积系统一侧表现出来。 集中于类型 $\mathcal N=1^*$和 $B_2$的 $A$理论，我们阐明了关于能隙真空结构、每个真空中实现的（广义）对称性和自发破缺模态不变性的意义。 显示英文摘要

摘要： Global variants of four-dimensional gauge theories are specified by their spectrum of genuine Wilson-'t Hooft line operators. The choice of global variant has significant consequences when spacetime is taken to be $\mathbb{R}^3 \times S^1$. We focus on $\mathcal N=1^*$ theories, which are closely connected to twisted elliptic Calogero-Moser systems. We establish, on general grounds, how this gauge-theoretic topological data manifests itself on the integrable system side by introducing a notion of global variants for complex many-body integrable systems associated with Lie algebras. Focusing on $\mathcal N=1^*$ theories of type $A$ and $B_2$, we elucidate the implications for the structure of gapped vacua, the emergent (generalized) symmetries realized in each vacuum, and the action of spontaneously broken modular invariance.