arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1009.2629hep-th
收藏

CP ^{ N-1 }西格玛模型中的θ-真空和大N极限

Theta-vacuum and large N limit in CP^{N-1} sigma models

Miguel Aguado, Manuel Asorey

备注：
v2: 25 pages, 4 eps figures, introduction expanded, matches published version
发表信息：
Nucl.Phys.B844:243-265,2011
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文用半经典方法、1/N展开和基于真空波泛函节点结构的论证重新分析了CP^{N-1}模型中真空能量密度的θ依赖性。1/N展开式与瞬子物理并不矛盾大体积V和大N参数的相互作用产生了具有不同θ依赖性的两个机制，一个表现为稀释的瞬子气体，另一个由传统的大N图像主导，其中瞬子作为单圈有效作用的共振再现，即使在没有规则瞬变解的情况下。这两个区域的范围分别用质量间隙m × m^2 V << N和m^2 V >> N表示。小体积区m^2 V << N与边界物理学相关的物理效应有关，例如边缘态在量子霍尔效应中的主导作用，然而，在大N时，边缘态在热力学极限中不起任何作用。根据极限N -> \infty和V -> \infty的顺序，得到两种不同的理论;这是1/N = 0时相变的标志。

英文摘要：

The theta dependence of the vacuum energy density in CP^{N-1} models is re-analysed in the semiclassical approach, the 1/N expansion and arguments based on the nodal structure of vacuum wavefunctionals. The 1/N expansion is shown not to be in contradiction with instanton physics at finite (spacetime) volume V. The interplay of large volume V and large N parameter gives rise to two regimes with different theta dependence, one behaving as a dilute instanton gas and the other dominated by the traditional large N picture, where instantons reappear as resonances of the one-loop effective action, even in the absence of regular instantonic solutions. The realms of the two regimes are given in terms of the mass gap m by m^2 V << N and m^2 V >> N, respectively. The small volume regime m^2 V << N is relevant for physical effects associated to the physics of the boundary, like the leading role of edge states in the quantum Hall effect, which, however, do not play any role in the thermodynamic limit at large N. Depending on the order in which the limits N -> \infty and V -> \infty are taken, two different theories are obtained; this is the hallmark of a phase transition at 1/N = 0.

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。

↑