nLab mysterious duality




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 kk-torus T kT^k corresponds to the complex projective space P 2\mathbb{C}P^2 blown up at kk generic points. In particular, for k=1k = 1 this corresponds to type IIA string theory (via duality between M-theory and type IIA string theory). Type IIB corresponds to 1× 1\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 12\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 P 1\mathbb{C}P^1s in P 1×P 1\mathbb{C}P^1 \times \mathbb{C}P^1.


The original observation:

Relation to Borcherds algebras:

Relation to Hypothesis H via automorphisms of iterated cyclic loop spaces of the 4-sphere:


See also at:

Last revised on December 8, 2023 at 13:39:32. See the history of this page for a list of all contributions to it.