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duality in string theory

Contents

Idea

Whatever it is otherwise, string theory turns out to be an organizational principle that subsumes a wealth of effective quantum field theories together with hints for their UV-completion. As such, string theory reveals a multitude of equivalences between superficially very different-looking (classes of) quantum field theories, or between various limits (notably strong/weak coupling limits) of various different-looking quantum field theories. Large classes of these equivalences go by the name of “dualities”:

Then there are the “string-string dualities”, notably the

Then there are the

There is also

Overview

under construction

S-duality in string theory

reduction from 11delectric σ-modelweak/strong coupling dualitymagnetic σ-model
M2-brane in 11d sugra EFT\leftarrowelectric-magnetic duality\rightarrowM5-brane in 11d sugra EFT
HW reduction
\downarrow on orientifold K3×S 1// 2\times S^1//\mathbb{Z}_2\downarrow on orientifold K3×S 1// 2\times S^1//\mathbb{Z}_2
F1-brane in heterotic supergravity\leftarrowS-duality\rightarrowblack string in heterotic sugra
HW reduction
\downarrow on orientifold T4×S 1// 2 \times S^1//\mathbb{Z}_2\downarrow on orientifold T4×S 1// 2 \times S^1//\mathbb{Z}_2
F1-brane in heterotic supergravity\leftarrowS-duality\rightarrowblack string in type IIA sugra
KK reduction
\downarrow on K3×S 1\times S^1\downarrow on K3×S 1\times S^1
F1-brane in IIA sugra\leftarrowS-duality\rightarrowblack string in heterotic sugra
KK reduction
\downarrow on T 4×S 1T^4\times S^1\downarrow on T 4×S 1T^4 \times S^1
F1-brane in IIA sugra\leftarrowS-duality\rightarrowblack string in type IIA sugra
F-reduction\updownarrow T-duality on S 1S^1
F1-brane in IIB sugra\leftarrowS-duality\rightarrowD1-brane in 10d IIB sugra
U-duality\updownarrow T-duality on T 2T^2
D3-brane in IIB sugra\leftarrowS-duality\rightarrowD3-brane in IIB sugra

gauge theory induced via AdS-CFT correspondence

M-theory perspective via AdS7-CFT6F-theory perspective
11d supergravity/M-theory
\;\;\;\;\downarrow Kaluza-Klein compactification on S 4S^4compactificationon elliptic fibration followed by T-duality
7-dimensional supergravity
\;\;\;\;\downarrow topological sector
7-dimensional Chern-Simons theory
\;\;\;\;\downarrow AdS7-CFT6 holographic duality
6d (2,0)-superconformal QFT on the M5-brane with conformal invarianceM5-brane worldvolume theory
\;\;\;\; \downarrow KK-compactification on Riemann surfacedouble dimensional reduction on M-theory/F-theory elliptic fibration
N=2 D=4 super Yang-Mills theory with Montonen-Olive S-duality invariance; AGT correspondenceD3-brane worldvolume theory with type IIB S-duality
\;\;\;\;\; \downarrow topological twist
topologically twisted N=2 D=4 super Yang-Mills theory
\;\;\;\; \downarrow KK-compactification on Riemann surface
A-model on Bun GBun_G, Donaldson theory

\,

gauge theory induced via AdS5-CFT4
type II string theory
\;\;\;\;\downarrow Kaluza-Klein compactification on S 5S^5
\;\;\;\; \downarrow topological sector
5-dimensional Chern-Simons theory
\;\;\;\;\downarrow AdS5-CFT4 holographic duality
N=4 D=4 super Yang-Mills theory
\;\;\;\;\; \downarrow topological twist
topologically twisted N=4 D=4 super Yang-Mills theory
\;\;\;\; \downarrow KK-compactification on Riemann surface
A-model on Bun GBun_G and B-model on Loc GLoc_G, geometric Langlands correspondence

References

Original articles

The original article suggesting the relation of 11d sugra to string theory is

An original article collecting all the weak/strong electric/magnetic dualities is

Surveys and lecture notes

A general survey is

A detailed discussion of dualities induced on K3-compactifications is in

Revised on December 20, 2014 01:42:37 by Urs Schreiber (127.0.0.1)