S-duality

S-duality

In theoretical physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling 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 and magnetic fields (and the electrically charged particles with magnetic monopoles).

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 the SO(32) heterotic string theory with the coupling constant 1/g. Perhaps most amazing are the S-dualities of type IIA string theory and E8 heterotic 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. the Ising model for Z2, the Potts model for Zn, the XY model for U(1) ), then its dual via the Kramers-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 charges.

See also

* T-duality
* U-duality
* S-duality (homotopy theory)
* Jordan-Wigner transformation


Wikimedia Foundation. 2010.

См. также в других словарях:

  • Duality — may refer to: Contents 1 Mathematics 2 Philosophy, logic, and psychology 3 Science 3.1 Electrical and mechanical …   Wikipedia

  • Duality principle — or principle of duality may refer to: Duality (projective geometry) Duality (order theory) Duality principle (Boolean algebra) Duality principle for sets Duality principle (optimization theory) Lagrange duality Duality principle in functional… …   Wikipedia

  • Duality (film) — Duality Directed by Mark Thomas Dave Macomber Starring Dave Macomber Mark Thomas Stephen Muraoka …   Wikipedia

  • Duality (Ra album) — Duality Studio album by Ra Released June 21, 2005 (U.S.) Recorded …   Wikipedia

  • Duality of structure — is one of Anthony Giddens coined phrases and main propositions in his explanation of structuration theory. The basis of the duality lies in the relationship the Agency has with the Structure. In the duality, the Agency has much more influence on… …   Wikipedia

  • Duality (сингл группы Slipknot) — Duality Сингл Vol. 3: The Subliminal Verses» Выпущен 4 мая, 2004 Формат CD Записан 2004 Жанр хард кор Длительн …   Википедия

  • Duality — совместный альбом Лизы Джеррард и Питера Бурка. Duality сингл группы Slipknot. Duality торговая марка корпорации Sony …   Википедия

  • Duality — Du al i*ty, n. [L. dualitas: cf. F. dualit[ e].] The quality or condition of being two or twofold; dual character or usage. [1913 Webster] …   The Collaborative International Dictionary of English

  • Duality — est le titre du premier single tiré de l album Vol. 3: (The Subliminal Verses), du groupe Slipknot. Portail de la musique Catégorie : Single musical sorti en 2003 …   Wikipédia en Français

  • duality — index duplicity Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • duality — late 14c., from O.Fr. dualité (14c.), from L.L. dualitas, from L. dualis (see DUAL (Cf. dual)) …   Etymology dictionary


Поделиться ссылкой на выделенное

Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку»