arXiv 1101.56862011-01hep-thhep-lat

随机威尔逊圈、简化模型和大D展开

Randomized Wilson loops, reduced models and the large D expansion

Oleg Evnin

备注：: 16 pages; v3: commentary further expanded, published version
发表信息：: Nucl. Phys. B 853 (2011) 461--474
DOI：: 10.1016/j.nuclphysb.2011.08.007

摘要：

简化模型是矩阵积分，被认为与规范理论的大N极限有关。已知当矩阵D的数目（对应于规范理论中的时空维数）变大时，这些积分会进一步简化。尽管这个极限似乎对计算标准矩形威尔逊圈（它总是从D中挑出两个方向）没有什么用处，但可以为随机威尔逊圈（其中所有D方向的贡献相等）定义一个有意义的大D极限。在这篇文章中，这种方法的概念验证演示给出了最简单的简化模型（原始的江口河合模型）和最简单的随机化的威尔逊圈（布朗和随机游动）。由此产生的平均威尔逊圈显示出强烈地让人联想到面积定律的尺度行为。

英文摘要：

Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. These integrals are known to simplify further when the number of matrices D (corresponding to the number of space-time dimensions in the gauge theory) becomes large. Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi-Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.

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。

摘要：

英文摘要：

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