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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 (i.e., is empty). 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 representing spacetime.
The concept of AdS is not of much interest in general relativity beyond some theoretical exploration, but its duality with conformal field theory is of interest because some quantum theories can be addressed using these two different mathematical approaches, offering of two means of solving problems: if solving a particular problem using one of the two methods is overly difficult, the other method can be utilized.