论文标题
$ 4 $ D ABELIAN LATTICE GAUGE理论的拓扑方面与$θ$参数
Topological aspects of $4$D Abelian lattice gauge theories with the $θ$ parameter
论文作者
论文摘要
我们研究了具有$θ$ Angle的四维$ u（1）$量规理论，该理论最初是由Cardy和Rabinovici提出的。众所周知，由于电气和磁性电荷颗粒的存在，该模型具有丰富的相图。我们讨论了该模型在$θ=π$下的倾斜限制阶段的拓扑性质，并展示其外观如何与异常约束保持一致。我们还通过测量其一部分对称性的一部分来构建$ sl（2，\ mathbb {z}）$从Cardy-Rabinovici模型中构造出来的自我双重理论。这种自二性具有与重力的混合异常的混合异常，并且它对相图的含义被发现。由于该模型与$ SU（N）$ Yang-Mills理论具有相同的全球对称性和H Hooft Anomaly，研究其拓扑方面将为我们提供更多的提示，以探索具有非零$θ$ ANGLE的非亚伯仪理论的可能动态。
We study a four-dimensional $U(1)$ gauge theory with the $θ$ angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at $θ=π$, and show how its appearance can be consistent with the anomaly constraint. We also construct the $SL(2,\mathbb{Z})$ self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed 't Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and 't Hooft anomaly with those of $SU(N)$ Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-Abelian gauge theories with nonzero $θ$ angles.
