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Encyclopedia > Mirror symmetry

In physics and mathematics, mirror symmetry is a surprising relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of string theory. More specifically, mirror symmetry relates two manifolds M and W whose Hodge numbers The willingness to question previously held truths and search for new answers resulted in a period of major scientific advancements, now known as the Scientific Revolution. ... Mathematics is the study of quantity, structure, space and change. ... In mathematics, a Calabi-Yau manifold is a compact K hler manifold with a vanishing first Chern class. ... String theory is a physical model whose fundamental building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points (particles) that were the basis of most earlier physics. ... In mathematics, Hodge theory is the study of the consequences for the algebraic topology of a smooth manifold M of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M. It was developed by W. V. D. Hodge in the 1930s as an extension...

h1,1 and h1,2

are swapped; string theory compactified on these two manifolds can be proved to be lead to identical physical phenomena.


The discovery of mirror symmetry is connected with names such as Brian Greene, Ronen Plesser, Philip Candelas, Monika Lynker, Rolf Schimmrigk and others. Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality: the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus. The simultaneous action of T-duality on all three dimensions of this torus is equivalent to mirror symmetry. Brian Greene at Harvard Dr. Brian Greene (born February 9, 1963) is a physicist and one of the worlds foremost string theorists. ... American theoretical physicist who works on string theory. ... Shing-Tung Yau (丘成桐; Pinyin: Qīu Chéngtóng; born April 4, 1949) is a prominent mathematician working in differential geometry, and involved in the theory of Calabi-Yau manifolds. ... T-duality is a symmetry of string theory, relating type IIA and type IIB string theory, and the two heterotic string theories. ... In mathematics, in particular in topology, a fiber bundle is a space which locally looks like a product of two spaces but may possess a different global structure. ... Geometry In geometry, a torus (pl. ...


Mirror symmetry allowed the physicists to calculate many quantities that seemed virtually incalculable before, by invoking the "mirror" description of a given physical situation, which can be often much easier. Mirror symmetry has also become a very powerful tool in mathematics, and although mathematicians have proved many rigorous theorems based on the physicists' intuition, a full mathematical understanding of the phenomenon of mirror symmetry is lacking. One possible mathematical framework is provided by the homological mirror symmetry conjecture. Homological mirror symmetry is a mathematical conjecture by Fields medalist Maxim Kontsevich that seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists. ...


  Results from FactBites:
 
Mirror symmetry - Wikipedia, the free encyclopedia (272 words)
The discovery of mirror symmetry is connected with names such as Lance Dixon, Wolfgang Lerche, Cumrun Vafa, Nicholas Warner, Brian Greene, Ronen Plesser, Philip Candelas, Monika Lynker, Rolf Schimmrigk and others.
Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality: the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus.
Mirror symmetry has also become a very powerful tool in mathematics, and although mathematicians have proved many rigorous theorems based on the physicists' intuition, a full mathematical understanding of the phenomenon of mirror symmetry is lacking.
Reflection symmetry - Wikipedia, the free encyclopedia (371 words)
Reflection symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.
The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical.
The triangles with this symmetry are isosceles, the quadrilaterals with this symmetry are the kites and the isosceles trapezoids.
  More results at FactBites »

 
 

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