### 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 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.

(*mathematics,physics*)
**Further reading:**

https://en.wikipedia.org/wiki/Anti-de_Sitter_space

https://en.wikipedia.org/wiki/De_Sitter_space

https://en.wikipedia.org/wiki/De_Sitter_universe

http://www.quantumfieldtheory.info/dS_and_AdS_spaces.pdf

**Referenced by page:**

holographic duality

Index