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Anti-self-dual connections over the $5$D Heisenberg group and the twistor method by Ren, Guangzhen; Wang, Wei is a scholarly article available to read on EtoBox.

What is Anti-self-dual connections over the $5$D Heisenberg group and the twistor method about?

In this paper, we introduce notions of $\alpha$-planes in $5$D complex Heisenberg group and the twistor space as the moduli space of all $\alpha$-planes. So we can define an anti-self-dual (ASD) connection as a connection flat over all $\alpha$-planes. This geometric approach allows us to establish Penrose-Ward correspondence between ASD connections over $5$D complex Heisenberg group and a class of holomorphic vector bundles on the twistor space. By Atiyah-Ward ans\"{a}tz, we also construct a family of ASD connections on $5$D complex Heisenberg group. When restricted to $5$D real Heisenberg group, the flat model of $5$D contact manifolds, an ASD connection satisfies the horizontal part of the contact instanton equation introduced by physicists.

Author

Ren, Guangzhen; Wang, Wei

Published

2021

Language

EN