论文标题
4D中自偶晶格理论的相结构
Phase structure of self-dual lattice gauge theories in 4d
论文作者
论文摘要
我们讨论了u（1）基于量规动作的改良小人公式的晶格量规理论模型，该模型允许耦合到玻色孔和磁性物质。该配方具有二元性，将电扇区和磁性扇形互相映射到彼此。我们提出了该模型的几种概括，并讨论了他们的“ hooft杂种异常”。一个特别有趣的一类理论是一种理论，其中电场和磁性领域与相同的动作结合在一起，因此，对于量规的特定值，该理论具有自动对称性对称性。自我对称对称性事实证明是一个组的生成器，该组是lattice Translation Symmetry Group的$ \ Mathbb Z_4 $的中心扩展。当恰好有一个磁性和一个磁性的玻色子时，最简单的情况是数值模拟的情况。我们详细讨论了该理论的相结构以及自偶像对称性的性质。使用系统的合适世界表示，我们介绍了支持猜想相图的数值模拟结果。
We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their 't~Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of $\mathbb Z_4$ by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.
