YANG-MILLS INSTANTONS ON ALE GRAVITATIONAL INSTANTONS
YANG-MILLS INSTANTONS ON ALE GRAVITATIONAL INSTANTONS
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DOI：
10.1007/bf01444534
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发表时间：
1990-01-01
影响因子：
1.4
通讯作者：
NAKAJIMA, H
中科院分区：
文献类型：
--
作者：
KRONHEIMER, PB;NAKAJIMA, H
Atiyah、Drinfeld、Hitchin和Manin在[ADHM]中讨论了S4上自对偶或反自对偶杨-米尔斯方程的解的构造或描述问题。所谓的ADHM构造将问题简化为求解某些有限维矩阵的二次方程，从而将问题转化为“代数”。在[Bu]和[Ki]中分别从另一个角度描述了流形~--fi 2上的解的类似构造。本文将描述一种”ADHM构造”，它产生另一类流形（[Kr]中研究的ALE引力瞬子）上的解，并简要地总结由通常的ADHM描述所产生的分类定理。我们将研究R 4上的联络而不是$4：通过关于奇点可移除性的乌伦贝克定理，R 4上的有限作用解扩展到紧化。因此，为了我们的目的，杨-米尔斯瞬子将意味着有限作用量反自对偶联系。结构群总是酉群。ADHM结构产生一个瞬子
The problem of constructing or describing the solutions of the self-dual or antiself-dual Yang-Mills equations on S 4 was addressed by Atiyah, Drinfeld, Hitchin, and Manin in [ADHM]. The so-called ADHM construction reduces the problem to the solution of a quadratic equation for certain finite-dimensional matrices, so translating the problem into" algebra". A similar construction is described for solutions on the manifold~--fi2 in [Bu], and from another point of view in [Ki]. In this paper we shall describe an" ADHM construction" which produces solutions on another family of manifolds, the" ALE gravitational instantons", which were studied in [Kr].Let us briefly summarize the classification theorem which results from the usual ADHM description. We shall work with connections on R 4 rather than $4: by Uhlenbeck's theorem on the removability of singularities, finite action solutions on R 4 extend to the compactification. Thus for our purposes, a Yang-Mills instanton will mean a finite-action anti-self-dual connection. The structure group will always be the unitary group. The ADHM construction produces an instanton