The Compatibility between the Higher Dimensions Self Duality and the Yang-Mills Equation of Motion

Abstract

We study the compatiblity between the higher dimension dualities and the Yang-Mills equation of motion. Taking a 't Hooft solution as a starting point, we come to the conclusion that for only 4 dimensions the self duality implies the equation of motion for generic instanton size. Whereas in higher dimensions, the self duality is compatable with the equation of motion, approximately, for small instanton size i.e. the zero curvature condition. At the mathematical level, the self duality is still useful since it transforms a second order into a first order differential equation.