Duality transformations of Abelian and non-Abelian gauge fields

Duality transformations, i.e., rotations of electric and magnetic fields into each other, are implementable by a time-local generator for source-free Maxwell theory in an arbitrary spacetime metric. The Maxwell action $\int (E^2-B^2)$ as well as the stress tensor components, e.g., $E^2+B^2$, are duality invariant and the generator is conserved. In the formally analogous Yang-Mills case, duality transformations cannot even be consistently implemented.