The Yang–Mills–Higgs functional on complex line bundles: Asymptotics for critical points

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-02 DOI:10.1515/acv-2023-0064

Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi

引用次数: 0

Abstract

We consider a gauge-invariant Ginzburg–Landau functional (also known as Abelian Yang–Mills–Higgs model), on Hermitian line bundles over closed Riemannian manifolds of dimension n ≥ 3

{n\geq 3}

. Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points in the London limit. After a convenient choice of the gauge, we show compactness of finite-energy critical points in Sobolev norms. Moreover, thanks to a suitable monotonicity formula, we prove that the energy densities of critical points, rescaled by the logarithm of the coupling parameter, converge to the weight measure of a stationary, rectifiable varifold of codimension 2.

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复线束上的杨-米尔斯-希格斯函数：临界点渐近

我们考虑在维数为 n ≥ 3 {n\geq 3} 的封闭黎曼流形上的赫米线束上的轨距不变金兹堡-朗道函数（也称为阿贝尔杨-米尔斯-希格斯模型）。假定耦合参数有对数能量约束，我们研究伦敦极限临界点的渐近行为。在方便地选择了量规之后，我们证明了有限能量临界点在索波列夫规范中的紧凑性。此外，得益于一个合适的单调性公式，我们证明了临界点的能量密度经耦合参数的对数重估后，会收敛到一个静止的、可整流的、标度为 2 的变折点的权重度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.