Multiple instantons representing higher-order Chern-Pontryagin classes (Q1374773)

The authors rigorously prove the existence of a topological charge \(N\) self-dual multi-instanton axially symmetric solution to the \(SO_{\pm}(4p)\) Yang-Mills model in \(4p\) dimensions. They study a nonlinear variational equation defined on the Poincaré half plane to establish the existence of such \(N\)-instanton solutions. These solutions are the first known instantons, with the Chern-Pontryagin index greater than one, of the Yang-Mills model in higher dimensions.