Astrophysics (Index)About

anti-de Sitter space

(AdS)
(type of curved space)

Anti-de Sitter space (AdS) is a type of mathematical object of interest in physics, in particular because it is used by a type of physical theory that is a dual of conformal field theory, the duality being termed the holographic principle. An AdS is a particular kind of manifold, a type of mathematical object (the type being defined by a set of axioms) that shares some specific qualities of space as we imagine it, aka Euclidean space. An AdS is curved with a uniform negative curvature, and a universe following the principles of general relativity could be an AdS, if it contains no mass (is empty in that regard) and has that curvature. A de Sitter space is the same except with a uniform positive curvature and a de-Sitter space in two dimensions is a sphere, the de-Sitter universe consists of a de Sitter space with four dimensions. The concept of AdS is not of much interest in general relativity beyond some theoretical exploration, but the fact that it forms the duality with conformal field theory is of interest as some quantum theories can be addressed using the two different mathematical approaches, offering two means of solving problems, the easier method depending on the specifics of the problem.


(mathematics,physics)
Further reading:
http://en.wikipedia.org/wiki/Anti-de_Sitter_space
http://en.wikipedia.org/wiki/De_Sitter_space
http://en.wikipedia.org/wiki/De_Sitter_universe
http://www.quantumfieldtheory.info/dS_and_AdS_spaces.pdf

Referenced by pages:
holographic duality

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