Anti-self-dual connections over the 5D Heisenberg group and the twistor method
Anti-self-dual connections over the 5D Heisenberg group and the twistor method
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DOI：
10.1016/j.geomphys.2022.104699
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发表时间：
2021-03
影响因子：
1.5
通讯作者：
Guangzhen Ren;Wei Wang
中科院分区：
文献类型：
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作者：
Guangzhen Ren;Wei Wang
通过在5D复海森堡群中引入α-平面的概念和扭量空间作为所有α-平面的模空间，我们可以定义反自对偶（ASD）联络作为所有α-平面上的联络平坦。这种几何方法使我们能够建立5D复海森堡群上的ASD连接和扭量空间上的一类全纯向量丛之间的Penrose-Ward对应。通过Atiyah-Ward ansätz，我们还构造了5D复Heisenberg群上的ASD联络.当限制到5D真实的海森堡群，5D接触流形的平坦模型时，ASD联络满足接触瞬子方程的水平部分。
By introducing notions of anα-plane in the 5D complex Heisenberg group and the twistor space as the moduli space of allα-planes, we can define an anti-self-dual (ASD) connection as a connection flat over allα-planes. This geometric approach allows us to establish the Penrose-Ward correspondence between ASD connections over the 5D complex Heisenberg group and a class of holomorphic vector bundles on the twistor space. By Atiyah-Ward ansätz, we also construct ASD connections on the 5D complex Heisenberg group. When restricted to the 5D real Heisenberg group, the flat model of 5D contact manifolds, an ASD connection satisfies the horizontal part of the contact instanton equation.