论文标题
晶格Abelian仪表理论中的分数拓扑费
Fractional topological charge in lattice Abelian gauge theory
论文作者
论文摘要
我们通过概括lüscher的收缩来构建一个非平凡的$ u（1）/\ mathbb {z} _q $ principal Bundle〜$ t^4 $，从紧凑型$ u（1）$ lattice Gauge Field中构建lüscher的收缩，从而使Cocycle条件构成cococycle条件，从而包含$ \ Mathbb {Z} _Q $ elements（t the t the t 〜houff flux）。该构造需要在晶格仪场配置上具有可接纳性条件。从如此构造的过渡函数中，我们具有分数拓扑电荷，即$ \ mathbb {z} _q $一型一型仪表不变，在晶格时间反转转换下。假设将真空角$θ\重新缩放为qθ$，我们的构造提供了$ \ m athbb {z} _q $一级对称性的混合't〜hooft异常的晶格实现$θ=π$，由本田和塔尼扎基研究[J。高能量物理。 \ textbf {12}，154（2020）]在连续框架中。
We construct a non-trivial $U(1)/\mathbb{Z}_q$ principal bundle on~$T^4$ from the compact $U(1)$ lattice gauge field by generalizing Lüscher's constriction so that the cocycle condition contains $\mathbb{Z}_q$ elements (the 't~Hooft flux). The construction requires an admissibility condition on lattice gauge field configurations. From the transition function so constructed, we have the fractional topological charge that is $\mathbb{Z}_q$ one-form gauge invariant and odd under the lattice time reversal transformation. Assuming a rescaling of the vacuum angle $θ\to qθ$ suggested from the Witten effect, our construction provides a lattice implementation of the mixed 't~Hooft anomaly between the $\mathbb{Z}_q$ one-form symmetry and the time reversal symmetry in the $U(1)$ gauge theory with matter fields of charge~$q\in2\mathbb{Z}$ when $θ=π$, which was studied by Honda and Tanizaki [J. High Energy Phys. \textbf{12}, 154 (2020)] in the continuum framework.
