# Why can AdS/CFT correspondence be applied to condensed matter systems when their space is not anti-deSitter?

The AdS/CFT correspondence postulates a duality between string theory of gravity and a CFT on an AdS background. This duality is employed in some condensed matter systems. I was wondering why it is applicable here when the condensed matter system in a laboratory is described by a quantum field theory that doesn't reside in AdS space - our space isn't AdS. Keep in mind I have studied general relativity and quantum field theory but not string theory.

• AdS/CFT correspondance is a duality between a gauge theory (a QFT) and a gravitational theory. A condensed matter system is then on the "gauge" side. – Kosm Feb 13 at 9:35
• Usually the idea is to convert a strongly-coupled condensed-matter system into a CFT (on Minkowski spacetime), which can then be translated into an AdS gravitational system. – probably_someone Feb 13 at 10:34

E.g. the nost famous case is the equivalence of the $$\mathcal{N}=4$$ supersymmetric Yang-Mills theory in the 4-dimensional Minkowski spacetime (which is CFT) with the Type IIb string theory in $$AdS_5\times S_5$$.
One of the most basic signs of the equivalence is that the conformal group of the $$d$$-dimensional Minkowski spacetime $$SO(2,d)$$ is exactly the isometry group of the $$d+1$$-dimensional AdS.