G2-instantons on the ALC members of the \(\mathbb {B}_7\) family

IF 0.6 3区 数学 Q3 MATHEMATICS
Jakob Stein, Matt Turner
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引用次数: 0

Abstract

Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian \(G_2\)-instantons on every member of the asymptotically locally conical \(\mathbb {B}_7\)-family of \(G_2\)-metrics on \(S^3 \times \mathbb {R}^4 \), and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT \(\mathbb {R}^4\), fibred over \(S^3\) in an adiabatic limit.

在\(\mathbb {B}_7\)家族的ALC成员的G2-instantons
利用共齐性一对称构造了一个非阿贝尔的双参数族 \(G_2\)-在渐近局部圆锥的每一成员上的实例 \(\mathbb {B}_7\)-家族 \(G_2\)-metrics on \(S^3 \times \mathbb {R}^4 \),并对得到的解进行分类。这些解可以被描述为由产生渐近圆光纤的杀死向量场引起的单参数阿贝尔瞬子族的扰动。一般来说,这些扰动对模型呈指数衰减,但我们发现了一个单参数的瞬子族具有多项式衰减。此外,我们将双参数族与Taub-NUT上反自对偶实例的显式双参数族的提升联系起来 \(\mathbb {R}^4\),纤维覆盖 \(S^3\) 在绝热极限下。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
70
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.
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