论文标题
通过持续同源性限制非亚伯晶格量规理论
Confinement in non-Abelian lattice gauge theory via persistent homology
论文作者
论文摘要
我们通过持续的同源性研究了SU（2）晶格量规理论中限制和解束阶段的结构，这使我们可以访问由给定数据构建的组合对象的层次结构的拓扑结构。具体而言，我们使用追踪的Polyakov环，拓扑密度，载体含量为代数场以及电场和磁场的过滤。这允许全面限制。特别是，拓扑密度形成空间块，显示出intsanton-dyons的经典概率分布的特征。位于随机位置的良好分离的对起的签名按照固体代数字段进行编码，遵循激体外观概率的半经典温度依赖性。 Debye筛选在持续的同源性中可见电场和磁场之间的区分，并在大型耦合下发音。所有使用的构造都是没有对所研究配置的先验假设的量规不变的。这项工作展示了迄今为止几乎没有探索的统计和量子物理学研究的持久性同源性的多功能性。
We investigate the structure of confining and deconfining phases in SU(2) lattice gauge theory via persistent homology, which gives us access to the topology of a hierarchy of combinatorial objects constructed from given data. Specifically, we use filtrations by traced Polyakov loops, topological densities, holonomy Lie algebra fields, as well as electric and magnetic fields. This allows for a comprehensive picture of confinement. In particular, topological densities form spatial lumps which show signatures of the classical probability distribution of instanton-dyons. Signatures of well-separated dyons located at random positions are encoded in holonomy Lie algebra fields, following the semi-classical temperature dependence of the instanton appearance probability. Debye screening discriminating between electric and magnetic fields is visible in persistent homology and pronounced at large gauge coupling. All employed constructions are gauge-invariant without a priori assumptions on the configurations under study. This work showcases the versatility of persistent homology for statistical and quantum physics studies, barely explored to date.
