Electric-magnetic duality rotations and invariance of actions

For D = 4 theories of a single U(1) gauge held strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated a s an invariance of the actions. The symmetry is associated with duality rot ation acting directly on the gauge field. The rotation is constructed in Ra t space, and an extension to curved spaces is also given. It is non-local a nd non-covariant, yet generates off-shell extended transformation of the fi eld strength. The algebraic condition of Gaillard and Zumino turns out to b e a necessary and sufficient condition for the invariance of actions. It ma y be used as a guiding principle in constructing self-dual actions in strin g and held theories. (C) 1999 Elsevier Science B.V.