- S-duality
In theoretical
physics , S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, orM-theory . An S-duality transformation maps the states and vacua withcoupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory. This has permitted the use of perturbation theory, normally useful only for "weakly coupled" theories with g less than 1, to also describe the "strongly coupled" (g greater than 1) regimes of string theory, by mapping them onto dual, weakly coupled regimes.In the case of four-dimensional quantum field theories, S-duality was understood by
Ashoke Sen ,Nathan Seiberg , and others. In this context, it usually exchanges the electric andmagnetic field s (and the electrically charged particles withmagnetic monopole s).See
Montonen-Olive duality ,Seiberg duality .Many more examples come from string theory: S-duality relates
type IIB string theory with the coupling constant g to the same type IIB string theory with the coupling constant 1/g. Similarly,type I string theory with the coupling g is equivalent to theSO(32) heterotic string theory with the coupling constant 1/g. Perhaps most amazing are the S-dualities oftype IIA string theory and E8heterotic string theory with coupling constant g to the higher dimensional M-theory with a compact dimension of size g.S-duality has been rigorously shown to hold in some lattice models. It depends on the
Pontryagin dual group.In particular, in 2 dimensions, if the vertices can take on values in a
locally compact Abelian group G and the action/energy only depends on the edges (e.g. theIsing model for Z2, thePotts model for Zn, theXY model for U(1) ), then its dual via theKramers-Wannier duality to a model where the vertices take on values in the dual group G'.In 3 dimensions, such a model would be dual to a
lattice gauge model over the dual group G'.In 4 dimensions, a lattice gauge model with G as the
gauge group would be dual to a lattice gauge model with G' as the gauge group (with the electric and magnetic fields interchanged).S-duality typically exchanges local charges with
topological charge s.See also
*
T-duality
*U-duality
*S-duality (homotopy theory)
*Jordan-Wigner transformation
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