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)
What is called the mysterious duality in Vafa 00, Iqbal-Neitzke-Vafa 01 is a kind of “duality in string theory” in the form of a correspondence between toroidal KK-compactifications of M-theory and del Pezzo surfaces: Here M-theory on the $k$-torus $T^k$ corresponds to the complex projective space $\mathbb{C}P^2$ blown up at $k$ generic points. In particular, for $k = 1$ this corresponds to type IIA string theory (via duality between M-theory and type IIA string theory). Type IIB corresponds to $\mathbb{P}^1 \times \mathbb{P}^1$.
Moreover, the moduli of KK-compactifications of M-theory on rectangular tori are mapped to Kähler moduli of del Pezzo surfaces. The U-duality group of M-theory corresponds to a group of classical symmetries of the del Pezzo represented by global diffeomorphisms. The $\frac{1}{2}$-BPS brane charges of M-theory correspond to spheres in the del Pezzo, and their tension to the exponentiated volume of the corresponding spheres.
The S-duality of type IIB in 10 dimensions corresponds to the exchange of the two complex projective curves $\mathbb{C}P^1$s in $\mathbb{C}P^1 \times \mathbb{C}P^1$.
The original observation:
Cumrun Vafa, from slide 42 in: Mirror symmetry, Talk at String Theory at the Millennium, Caltech, January 2000 (slides html)
Amer Iqbal, Andrew Neitzke, Cumrun Vafa, A mysterious duality, (arXiv:hep-th/0111068)
Relation to Borcherds algebras:
Relation to Hypothesis H via automorphisms of iterated cyclic loop spaces of the 4-sphere:
review:
See also at:
Last revised on July 23, 2022 at 13:50:55. See the history of this page for a list of all contributions to it.