论文标题
持续的同源性作为中心涡流的探测和SU中的解解（2）晶格理论
Persistent homology as a probe for center vortices and deconfinement in SU(2) lattice gauge theory
论文作者
论文摘要
拓扑数据分析（TDA）是一个领域，该领域利用代数拓扑的工具和思想来提供可靠的方法来分析数据的几何和拓扑方面。 TDA的主要工具之一，持续的同源性，对数据的连通性和结构进行了定量描述，该数据的连接性和结构如何通过一系列量表进行查看。我们建议这是一种直接探测仪表理论中拓扑对象的手段。我们介绍了使用持久同源性以量规不变的方式检测SU（2）晶格量规理论中的中心涡旋的最新工作。我们介绍了持久性的基础知识，描述了我们的构建，并证明了结果对涡流很敏感。此外，我们讨论了如何通过简单的机器学习，可以利用由此产生的持久性通过有限尺寸的缩放来定量分析解密过渡，从而提供了证据，证明了涡旋在Yang-Mills理论中的限制方面的作用。
Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology, produces a quantitative description of how the connectivity and structure of data changes when viewed over a sequence of scales. We propose that this presents a means to directly probe topological objects in gauge theories. We present recent work on using persistent homology to detect center vortices in SU(2) lattice gauge theory configurations in a gauge-invariant manner. We introduce the basics of persistence, describe our construction, and demonstrate that the result is sensitive to vortices. Moreover we discuss how, with simple machine learning, one can use the resulting persistence to quantitatively analyse the deconfinement transition via finite-size scaling, providing evidence on the role of vortices in relation to confinement in Yang-Mills theories.
