Montonen-Olive duality
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In theoretical physics, Montonen-Olive duality is the oldest known example of S-duality or a strong-weak duality. It generalizes the electro-magnetic symmetry of Maxwell's equations.
In a four-dimensional theory with N=4 supersymmetry, which is the case where the Montonen-Olive duality applies, one obtains a physically equivalent theory if one replaces the coupling constant g by 1/g. This also involves an interchange of the electrically charged particles and magnetic monopoles. See also Seiberg duality.
In fact, there exists a larger symmetry SL(2,Z) where both g as well as theta-angle are transformed non-trivially.
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