Stability and energy identity for Yang–Mills–Higgs pairs
Stability and energy identity for Yang–Mills–Higgs pairs
复制标题
DOI：
10.1063/5.0130905
复制
发表时间：
2023-02
影响因子：
1.3
通讯作者：
Xiaoli Han;Xishen Jin;Yang Wen
中科院分区：
文献类型：
--
作者：
Xiaoli Han;Xishen Jin;Yang Wen
在本文中，我们研究了杨-米尔斯-希格斯泛函的临界点的性质，称为杨-米尔斯-希格斯对。我们首先考虑 S n ( n ≥ 4) 上向量丛上弱稳定的 Yang-Mills-Higgs 对的性质。当n≥4时，我们证明其希格斯场的范数为1，实际上是Yang-Mills联系。更准确地说，当 n ≥ 5 时，它的曲率消失。我们还使用泡颈分解来证明具有均匀有界能量的四维紧流形上的杨-米尔斯-希格斯对序列的能量恒等式。我们证明存在一个子序列，它平滑地收敛到杨-米尔斯-希格斯对，以测量具有杨-米尔斯连接的有限多个四维球体的模。
In this paper, we study the properties of the critical points of Yang–Mills–Higgs functional, which are called Yang–Mills–Higgs pairs. We first consider the properties of weakly stable Yang–Mills–Higgs pairs on a vector bundle over S n ( n ≥ 4). When n ≥ 4, we prove that the norm of its Higgs field is 1 and the connection is actually Yang–Mills. More precisely, its curvature vanishes when n ≥ 5. We also use the bubble-neck decomposition to prove the energy identity of a sequence of Yang–Mills–Higgs pairs over a four-dimensional compact manifold with uniformly bounded energy. We show there is a subsequence that converges smoothly to a Yang–Mills–Higgs pair up to gauge modulo finitely many four-dimensional spheres with Yang–Mills connections.