How to extract the dominant part of the Wilson loop average in higher representations
How to extract the dominant part of the Wilson loop average in higher representations
复制标题
如何在更高的表示中提取威尔逊循环平均值的主要部分
DOI：
10.1103/physrevd.100.014505
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
S. Kato and K.-I. Kondo
中科院分区：
文献类型：
--
作者：
R. Matsudo;A. Shibata;S. Kato and K.-I. Kondo
在以前的工作中，我们已经提出了一个新的制定的杨米尔斯理论的格点，使所谓的限制场得到的规范协变分解在夸克禁闭中起主导作用。该框架以规范无关的方式改进了阿贝尔投影。对于基本表象中的夸克，我们已经证明了弦张力中限制场占主导地位的一些数值证据，这意味着从威尔逊环的限制部分提取的弦张力再现了从原始威尔逊环提取的弦张力。然而，它是已知的，在更高的表示中，如果威尔逊环的限制部分是通过采用阿贝尔投影或场分解天真地以与基本表示相同的方式提取，则对于威尔逊环，不观察到限制场优势。因此，在本文中，我们专注于禁闭夸克在更高的表示。借助于Wilson环算子的非阿贝尔Stokes定理，我们提出了从限制场构造的合适的规范不变算子，以再现原Wilson环平均在更高表示下的正确行为.此外，我们进行晶格模拟测量夸克在更高的表示使用建议的运营商的静态潜力。我们发现，所提出的运营商很好地再现了原来的威尔逊回路平均的行为，即，与正确的弦张力值的静态电位的线性部分，这克服了发生在天真地应用阿贝尔投影威尔逊回路运营商更高的表示。
In previous works, we have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. This framework improves the Abelian projection in the gauge-independent manner. For quarks in the fundamental representation, we have demonstrated some numerical evidence for the restricted field dominance in the string tension, which means that the string tension extracted from the restricted part of the Wilson loop reproduces the string tension extracted from the original Wilson loop. However, it is known that the restricted field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this paper, therefore, we focus on the confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the behavior of the original Wilson loop average, namely, the linear part of the static potential with the correct value of the string tension, which overcomes the problem that occurs in naively applying Abelian projection to the Wilson loop operator for higher representations.