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It was established long ago that SO(2) electric-magnetic duality is an {\em off-shell} symmetry of the free Maxwell theory, i.e., that it leaves invariant the action and not just the equations of motion.
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1997
Cited alongside, same era.
C. Bunster and M. Henneaux, “Can (Electric-Magnetic) Duality Be Gauged?,” arXiv:1011.5889 [hep-th]
Cited in the paper.
C. Bunster and M. Henneaux, in preparation
Cited in the paper.
S. Deser, “No local Maxwell duality invariance,” arXiv:1012.5109 [hep-th]
Cited in the paper.