A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-07-16 DOI:10.1007/s10455-024-09954-z

Jaime Mendizabal

引用次数: 0

Abstract

We construct the hyper-Kähler moduli space of framed monopoles over \(\mathbb {R}^3\) for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence arbitrary symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.

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具有任意对称破缺的单极子模空间上的超凯勒度量

对于任何连通的、简单连通的、紧凑的、半简单的李群和任意质量与电荷，以及任意对称性破缺，我们都要构建\(\mathbb {R}^3\) 上有框单极的超凯勒模空间。为此，我们定义了一个具有适当渐近条件的成对构型空间，并进行了无限维商数构造。我们利用 b 和散射计算来研究相关的微分算子。

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.