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Mysterious duality
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In theoretical physics, mysterious duality, introduced by , concerns similarities between M-theory and del Pezzo surfaces. More specifically there is a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori (i.e. type II superstring theory on T 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 P 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 P C × P C, is connected with type IIB string theory in 10 dimensions. This conjecture was developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke. See Also
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