In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws (and perhaps all of them, if the conjecture is extended appropriately) describing M-theory on k-dimensional tori (i.e. type II superstring theory on T^{k − 1} if k is positive) on one side, and geometry of del Pezzo surfaces (for example, the cubic surfaces) on the other side. Theoretical physics is physics that employs mathematical models and abstractions rather than experimental processes. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... // Geometry In geometry, a torus (pl. ... In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. ... Jump to: navigation, search Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ... In mathematics, a del Pezzo surface is a complex two-dimensional Fano variety, i. ... A cubic surface is a projective variety studied in algebraic geometry. ...

The main observation is that the large diffeomorphisms of del Pezzo surfaces match the Weyl group of the U-duality group of the corresponding compactification of M-theory. The elements of the second homology of the del Pezzo surfaces are mapped to various BPS objects of different dimensions in M-theory. In mathematics and theoretical physics, a large diffeomorphism is a diffeomorphism that cannot be continuously connected to the identity diffeomorphism (because it is topologically non-trivial). ... In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is the subgroup of the isometry group of the root system generated by reflections through the hyperplanes orthogonal to the roots. ... U-duality is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ...

The complex projective plane CP² is related to M-theory in 11 dimensions. When k points are blown-up, the del Pezzo surface describes M-theory on a k-torus, and the exceptional del Pezzo surface, namely , is connected with type IIB string theory in 10 dimensions. In mathematics, the complex projective plane, usually denoted CP2, is the two-dimensional complex projective space. ... In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. ...

This conjecture was developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke from Harvard University. Cumrun Vafa is a leading string theorist from Harvard University where he started as a Harvard Junior Fellow. ... Jump to: navigation, search Harvard University is a private university in Cambridge, Massachusetts, USA, and a member of the Ivy League. ...

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