Astrophysics (Index)About

anti-de Sitter space

(type of curved space)

Anti-de Sitter space (AdS) is a type of mathematical object of interest in physics, in particular because it can underly a physical theory that is a dual of conformal field theory, this duality termed the AdS/CFT correspondence. 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. Among the additional defining characteristics of an AdS is a uniform negative curvature, and a universe following the principles of general relativity could be an AdS only if it contained no mass (is empty in that regard). A de Sitter space is the same except with a uniform positive curvature; a de-Sitter space in two dimensions is a sphere and a 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 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 more practical of the two methods depending on the specifics of the problem.

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Referenced by page:
holographic duality