general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
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”:
general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
under construction
gauge theory induced via AdS-CFT correspondence
M-theory perspective via AdS7-CFT6 | F-theory perspective |
---|---|
11d supergravity/M-theory | |
Kaluza-Klein compactification on | compactificationon elliptic fibration followed by T-duality |
7-dimensional supergravity | |
topological sector | |
7-dimensional Chern-Simons theory | |
AdS7-CFT6 holographic duality | |
6d (2,0)-superconformal QFT on the M5-brane with conformal invariance | M5-brane worldvolume theory |
KK-compactification on Riemann surface | double dimensional reduction on M-theory/F-theory elliptic fibration |
N=2 D=4 super Yang-Mills theory with Montonen-Olive S-duality invariance; AGT correspondence | D3-brane worldvolume theory with type IIB S-duality |
topological twist | |
topologically twisted N=2 D=4 super Yang-Mills theory | |
KK-compactification on Riemann surface | |
A-model on , Donaldson theory |
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
John Schwarz, Lectures on Superstring and M Theory Dualities, Nucl. Phys. Proc. Suppl. 55B:1-32, 1997 (arXiv:hep-th/9607201)
Michael Dine, String Theory Dualities [arXiv:hep-th/9609051]
Luis Alvarez-Gaumé, Frederic Zamora, Duality in Quantum Field Theory (and String Theory), AIP Conference Proceedings 423, 46 (1998) (arXiv:hep-th/9709180)
Stefan Forste, Jan Louis, Duality in String Theory, Nucl. Phys. Proc. Suppl. 61A:3-22, 1998 (arXiv:hep-th/9612192)
Ashoke Sen, Duality symmetries in string theory, Current Science Vol. 77, No. 12, 25 December 1999 (jstor:24104472)
Mike Duff, chapter 6 of The World in Eleven Dimensions: Supgergravity, Supermembranes and M-theory, IoP 1999
Joseph Polchinski, Dualities (arXiv:1412.5704)
More on dualities induced on K3-compactifications:
More in view of the landscape of string theory vacua:
Also
Discussion amplifying the role of category theory, and higher geometry is in
Last revised on February 14, 2023 at 05:16:16. See the history of this page for a list of all contributions to it.