On the Energy Spectrum of Yang-Mills Instantons over Asymptotically Locally Flat Spaces

In this paper we prove that over an asymptotically locally flat (ALF) Riemannian four-manifold the energy of an "admissible" SU(2) Yang-Mills instanton is always integer. This result sharpens the previously known energy identity for such Yang-Mills instantons over ALF geometries. Furthermore we demonstrate that this statement continues to hold for the larger gauge group U(2). Finally we make the observation that there might be a natural relationship between 4 dimensional Yang-Mills theory over an ALF space and 2 dimensional conformal field theory. This would provide a further support for the existence of a similar correspondence investigated by several authors recently.