anti-de Sitter space

Unfortunately, the noncompact dimensions have to form an anti-de Sitter space.

In this description, there is a small extra dimension that is a slice of anti-de Sitter space.

So far the conjecture only works in a special, saddle-shaped universe called Anti-de Sitter space.

The mathematical description of anti-de Sitter space generalizes the idea of curvature.

In mathematics, anti-de Sitter space is sometimes defined more generally as a space of arbitrary signature (p,q).

One can have an anti-de Sitter space (or a de Sitter space) in an arbitrary number of dimensions.

The metric on anti-de Sitter space is the metric induced from the ambient metric.

A coordinate patch covering part of the space gives the half-space coordinatization of anti-de Sitter space.

Bengtsson, Ingemar: Anti-de Sitter space.

Matsuda, H. A note on an isometric imbedding of upper half-space into the anti-de Sitter space.

Some authors define anti-de Sitter space as equivalent to the embedded sphere itself, while others define it as equivalent to the universal cover of the embedding.

In mathematics and physics, n-dimensional anti-de Sitter space, sometimes written , is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.

And so far, the connection Dr. Maldacena found only works in something called anti-de Sitter space (after the Dutch astronomer Willem de Sitter).

An anti-de Sitter space, in contrast, is a general relativity-like spacetime, where in the absence of matter or energy, the curvature of spacetime is naturally hyperbolic.

The AdS/CFT (anti-de Sitter space/conformal field theory) correspondence is an idea originally proposed by Juan Maldacena in late 1997.

More concretely, our universe is a five-dimensional anti-de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes.

There is a particularly important implication of the more precise mathematical description that differs from the analogy based heuristic description of de Sitter space and anti-de Sitter space above.

It also explains that Minkowski space, de Sitter space and anti-de Sitter space, as applied to general relativity, can all be thought of as five-dimensional versions of spacetime.

In an anti-de Sitter space, as in a de Sitter space, the extent of inherent spacetime curvature corresponds to the magnitude of the negative cosmological constant to which it is equivalent.

The generality of the concepts of de Sitter space and anti-de Sitter space make them useful in theoretical physics, particularly in string theory, that often assume a world with more than four dimensions.

Naturally, as the remainder of this article explains in technical detail, the general concepts described in this non-technical explanation of anti-de Sitter space have a much more rigorous and precise mathematical and physical description.

This criticism has been addressed to some extent by the AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter space asymptotics.

In the language of general relativity, anti-de Sitter space is a maximally symmetric, vacuum solution of Einstein's field equation with a negative (attractive) cosmological constant (corresponding to a negative vacuum energy density and positive pressure).

Note also that while an anti-de Sitter space would describe general relativity with a negative cosmological constant in five dimensions (four for spacetime and one for the effect of the cosmological constant), the idea is actually more general.

In the common analogy of an object causing a dip in a flat cloth, anti-de Sitter space has a curvature analogous to a flat cloth sitting on a saddle, with a very slight curvature because it is so large.