S Duality

Suppose now that a pair of theories A and B are S-dual. This means that if f denotes any physical observable and l denotes the coupling constant, then

(The expansion parameter a introduced earlier corresponds to l).
This duality, whose recognition was the first step in the current revolution, [6] generalizes the electric-magnetic symmetry of Maxwell theory. Since the Dirac quantization condition implies that the basic unit of magnetic charge is inversely proportional to the unit of electric charge, their interchange amounts to an inversion of the charge (which is the coupling constant).
S duality relates the type I theory to the HO theory and the IIB theory to itself. This explains the strong coupling behavior of those three theories.

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