# Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, etc.). To my understanding, an AdS space has constant negative curvature in a vacuum, which should yield an attractive universe, not one with accelerating expansion. An AdS space can be thought of as having a negative cosmological constant, while a universe with accelerating expansion would imply that such a constant be positive. Since we observe that our universe's expansion is accelerating, it seems that if anything, we should be seeking to model it as a de Sitter space.

Am I mistaken? What aspects of our universe do AdS spaces attempt to model?

• I have very little knowledge of GR, so I don't know much about this. But from the little that I had heard about AdS, I had exactly the same question/doubt as you. Nice question, I hope somebody answers. – Physics Llama Jun 30 '14 at 21:12
• – Qmechanic Jun 30 '14 at 21:17
• I came to this exact thing reading "The Black Hole War". I kept asking myself "where is the cosmic horizon", and when we got to the part where he should have explained this, the acceleration went in the opposite direction. I might still ask something if I can obtain some novelty, but before that I might have to re-read the latter chapters again. The theorists seem to be a mess regarding how dark energy has impacted their work. – Alan Rominger Sep 23 '14 at 1:45

The reason why the AdS/CFT correspondence is interesting is not that AdS space is supposed to describe our universe, which, as you have correctly pointed out, would lead to conflicts with experiments. In the context of the correspondence, a four-dimensional (conformal) field theory is mapped to a string theory living in an $AdS_5\times S^5$ space, although there exist generalizations in which the AdS part is of higher or lower dimension than five.
One may now ask what is so special about AdS space that allows for such a duality? One way to approach this is to point out the rich symmetry content of this kind of spacetime. The isometry group of Anti-de Sitter space is given by $SO(4,2)$, which is precisely the conformal group in four dimensions.