### 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

Index