A nonperturbative symmetry that relates the weak and strong coupling regimes of a quantum theory. In a gauge theory the inversion of the coupling is accompanied by the interchange of the electric and magnetic degrees of freedom [1]. When a θ-term is included in the Lagrangian there is an additional symmetry under θ → θ + 2π, and the theory is then invariant under τ → − 1/τ and τ → τ + 1, with
and g the coupling constant. These two transformations generate the SL(2, Z) group, or S-duality group [2]. Examples in which it is conjectured to be a symmetry: Four dimensional N = 4 supersymmetric Yang-Mills theory, where it is referred as Montonen-Olive duality [3]. In string theory : symmetry of the ten dimensional Type IIB superstring theory [4], it relates the Type I and heterotic SO(32) theories [5,6,7], in four dimensions it is a symmetry of the heterotic compactified on a 6- torus [8].
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Lozano, Y. (2004). S-Duality. In: Duplij, S., Siegel, W., Bagger, J. (eds) Concise Encyclopedia of Supersymmetry. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4522-0_470
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