I have it that this correspondence is only valid in a Universe made of Anti-de-Sitter space. Some web pages and videos talk as if it is valid in our Universe.

The anti Desitter metric itself works for any case where the geometry is a negative curvature. The conformal portion applies to the string theory portion of the metric.

 The positive curvature is covered via the De-Sitter spacetime. 

 The metric is particularly useful to allow string theory flexibility in regions of strong couplings such as the EH of a blackhole.

Edited December 4, 20223 yr by Mordred