nLab
duality in string theory

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”:

• T-duality, mirror symmetry

• S-duality, electric-magnetic duality

• U-duality .

There is also

• the relation between 11-dimensional supergravity and the various string theories, see

  • F-theory

• the AdS/CFT correspondence.

Overview

under construction

reduction from 11d	electric σ-model	weak/strong coupling duality	magnetic σ-model
	M2-brane in 11d sugra EFT	$\leftarrow$electric-magnetic duality$\to$	M5-brane in 11d sugra EFT
HW reduction
	$\downarrow$ on orientifold K3$\times S^1//{\mathbb{Z}}_2$		$\downarrow$ on orientifold K3$\times S^1//{\mathbb{Z}}_2$
	F1-brane in heterotic supergravity	$\leftarrow$S-duality$\to$	black string in heterotic sugra
HW reduction
	$\downarrow$ on orientifold T4$\times S^1//{\mathbb{Z}}_2$		$\downarrow$ on orientifold T4$\times S^1//{\mathbb{Z}}_2$
	F1-brane in heterotic supergravity	$\leftarrow$S-duality$\to$	black string in type IIA sugra
KK reduction
	$\downarrow$ on K3$\times S^1$		$\downarrow$ on K3$\times S^1$
	F1-brane in IIA sugra	$\leftarrow$S-duality$\to$	black string in heterotic sugra
KK reduction
	$\downarrow$ on $T^4\times S^1$		$\downarrow$ on $T^4\times S^1$
	F1-brane in IIA sugra	$\leftarrow$S-duality$\to$	black string in type IIA sugra
F-reduction	$\updownarrow$ T-duality on $S^1$
	F1-brane in IIB sugra	$\leftarrow$S-duality$\to$	D1-brane in 10d IIB sugra
		U-duality	$\updownarrow$ T-duality on $T^2$
	D3-brane in IIB sugra	$\leftarrow$S-duality$\to$	D3-brane in IIB sugra

Related concepts

• duality in physics

References

Original articles

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

• Edward Witten, String theory in various dimensions, Nucl.Phys.B443:85-126,1995 (arXiv:hep-th/9503124)

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

• Mike Duff, M-theory (the theory formerly known as string), Int.J.Mod.Phys. A11 (1996) 5623-5642 (arXiv:hep-th/9608117)

Surveys and lecture notes

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

• Paul Aspinwall, K3-surfaces and string duality (arXiv:hep-th/9611137)