arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0804.1534hep-lat
收藏

分数荷电威尔逊圈作为$CP^{N-1}$西格玛模型中$θ$依赖性的探针：瞬子与大N

Fractionally charged Wilson loops as a probe of $θ$-dependence in $CP^{N-1}$ sigma models: Instantons vs. large N

Patrick Keith-Hynes, H. B. Thacker

备注：
16 pages, 10 figures
发表信息：
Phys.Rev.D78:025009,2008
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

利用分数电荷威尔逊圈的行为研究了二维时空中$CP^1$、$CP^5$和$CP^9$西格玛模型的自由能密度$ε(θ)$对$θ$的依赖性.函数$ε(θ)$是从电荷$q=θ/2π$的威尔逊环的面积定律中提取的。对于$CP^1$，$ε(θ)$在$θ\approxπ$区域内是光滑的，并且在整个$0<θ<2π$范围内被稀释的瞬子气体很好地描述。对于$CP^5$和$CP^9$的能量表现出明显的尖点和离散的证据，退化真空在$θ= π$，预期从大$N$参数。对于$CP^9$，在整个范围$0<θ<π$内，$θ$依赖性与首阶大$N$预测$ε(θ)={1/2}χ_tθ^2$具有良好的定量一致性。

英文摘要：

The behavior of Wilson loops with fractional charge is used to study the $θ$-dependence of the free energy density $ε(θ)$ for the $CP^1$, $CP^5$, and $CP^9$ sigma models in two spacetime dimensions. The function $ε(θ)$ is extracted from the area law for a Wilson loop of charge $q=θ/2π$. For $CP^1$, $ε(θ)$ is smooth in the region $θ\approxπ$ and well-described by a dilute instanton gas throughout the range $0<θ<2π$. For $CP^5$ and $CP^9$ the energy exhibits a clear cusp and evidence for discrete, degenerate vacua at $θ= π$, as expected from large $N$ arguments. For $CP^9$ the $θ$-dependence is in good quantitative agreement with the leading order large $N$ prediction $ε(θ)={1/2}χ_tθ^2$ throughout the range $0<θ<π$.

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。

↑