  In this paper we prove that over an asymptotically locally flat (ALF)
Riemannian four-manifold the energy of an "admissible" SU(2) Yang--Mills 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.
