Strong-weak duality

In theoretical physics, S-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier.

In quantum field theory, S-duality generalizes a well known fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. One of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called N = 4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is closely related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality in quantum field theory is Seiberg duality, which relates two versions of a theory called N=1 supersymmetric Yang–Mills theory.

There are also many examples of S-duality in string theory. The existence of these string dualities implies that seemingly different formulations of string theory are actually physically equivalent. This led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single eleven-dimensional theory called M-theory.

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