阿贝尔色圈：非阿贝尔格点规范理论强耦合展开和对偶表示的新途径
Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory
摘要：
以SU（2）为例，我们提出了一种新的方法来研究非交换格点规范理论的强耦合级数和对偶表示。威尔逊规范作用量被写为“阿贝尔色循环”（ACC）的总和，其对应于色环周围的色空间中的循环。ACCs是复数，可以自由交换，使得强耦合级数和对偶表示可以像阿贝尔情形一样获得。利用SU（2）规范变量的一个合适的表示，我们整合出所有的原始规范链接，并确定在SU（2）的情况下的对偶变量的约束。我们证明了这种构造可以推广到SU（2）规范场中的交错费米子的情形。其结果是一个强耦合系列，所有的规范积分是已知的封闭形式，我们讨论其适用性可能的双重模拟。阿贝尔色循环的概念可以推广到其他非阿贝尔规范群，如SU（3）。
英文摘要：
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over "abelian color cycles" (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
