Do any and all 4D or 5D AdS satisfy AdS/CFT correspondence

[kodama]

does any and all 4-D 5-D AdS spaces always have a 3-d or 4-D (d-1) CFT corresponding ?

or are there 4D and 5D AdS where there is NO corresponding CFT?

i.e is it possible to posit a 4D (5D) space that is AdS that has no 3D (4D) CFT ?

since our universe is 4D, should AdS in 4D be studied with 3D CFT corresponding ?

 

[AndyW]

I can say that the answer to this question is not as straightforward as a simple yes or no. It depends on the specific properties and characteristics of the 4D or 5D AdS space in question.

In general, it is believed that any AdS space can have a corresponding CFT. This is known as the AdS/CFT correspondence, which is a fundamental principle in theoretical physics. However, there are certain cases where this correspondence may not hold true.

For example, if the AdS space has a very high curvature or is highly distorted, it may not have a corresponding CFT. Additionally, if the AdS space is not asymptotically AdS (meaning it does not approach flat space at infinity), then it may not have a corresponding CFT.

Furthermore, the dimensionality of the AdS space also plays a role. In 4D AdS, there is always a corresponding 3D CFT due to the AdS/CFT correspondence. However, in 5D AdS, there may not always be a corresponding 4D CFT. This is because the AdS/CFT correspondence only holds for a specific ratio of dimensions (specifically, one less dimension in the CFT than in the AdS space).

In summary, it is possible to posit a 4D (or 5D) AdS space that does not have a corresponding 3D (or 4D) CFT. However, these cases are not common and are usually associated with highly distorted or non-asymptotically AdS spaces. Therefore, studying AdS in 4D with a corresponding 3D CFT is generally a valid approach, but it may not always be applicable in all cases.