Mysterious Duality
A conjecture developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke in 2001, called "mysterious duality", concerns a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori (i.e. type II superstring theory on Tk − 1 for k > 0) on one side, and geometry of del Pezzo surfaces (for example, the cubic surfaces) on the other side. 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.
The complex projective plane P2(C) 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 P1(C) × P1(C), is connected with type IIB string theory in 10 dimensions.
Read more about this topic: M-theory
Famous quotes containing the word mysterious:
“There is nothing more mysterious than a TV set left on in an empty room. It is even stranger than a man talking to himself or a woman standing dreaming at her stove. It is as if another planet is communicating with you.”
—Jean Baudrillard (b. 1929)