When is the electro-magnetic duality $F \rightarrow \star F$ a symmetry of a theory? I know it holds for free Yang-Mills, but would for instance a Chern-Simons term break it or a coupling to matter? And is the duality a part of the Lorentz symmetry as they both mix electric and magnetic fields? So if a theory is Lorentz symmetric, is it also symmetric under the electro-magnetic duality?
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