论文标题
分数涡流，$ \ mathbb {z} _2 $量规理论和限制过渡
Fractional Vortices, $\mathbb{Z}_2$ Gauge Theory, and the Confinement-Deconfinement Transition
论文作者
论文摘要
在本文中，我们讨论了最近的3D XY模型，其最接近的邻居相互作用是$ \ cos（θ_i-θ_j）$（Ferromagnetic）和$ \ cos2（θ_i-θ_j）$（nematic）的混合物。该模型对具有整数和半刻涡流的理论是双重的。尽管两种类型的涡流都与非连接$ u（1）$ gauge字段（“ em”相互作用）相互作用，但半涡流与由$ \ mathbb {z} _2 _2 $ gauge字段介导的额外相互作用相互作用。我们将讨论一半涡流，威尔逊和't Hooff Loops及其相互统计数据的禁闭范围过渡。此外，我们将提出展示这些物理学的经典模型的量子版本。
In this paper we discuss the classical 3D XY model whose nearest-neighbor interaction is a mixture of $\cos(θ_i-θ_j)$ (ferromagnetic) and $\cos2(θ_i-θ_j)$ (nematic). This model is dual to a theory with integer and half-integer vortices. While both types of vortices interact with a non-compact $U(1)$ gauge field (the "EM" interaction), the half-vortices interact with an extra interaction mediated by a $\mathbb{Z}_2$ gauge field. We shall discuss the confinement-deconfinement transition of the half-integer vortices, the Wilson and the 't Hooft loops and their mutual statistics in path integral language. In addition, we shall present a quantum version of the classical model which exhibits these physics.
