Is Ads/CFT correspondance the same as gauge /gravity duality?
These terms are used quite loosely and often interchanged. Ads/cft is an example of a gauge/gravity or gauge/string duality. There are various examples of ads/cft as well. ads5/cft4 (maldacena), ads4/cft3 etc (polyakov-klebanov) etc
From the little I know in gauge theory , QCD has asymptotic freedom . Does this mean that it is not conformally invariant ? If so , how there is Ads\CFT correspondance between QCD and string theory?
I think AdS/CFT is only an APPROXIMATIVE correspondence in QCD.
Basically, gauge/gravity duality is a generalization of the original AdS/CFT conjecture, which can be thought of as a manifestation of the holographic principle. The original concept was a correspondence between an N=4 Supersymmetric Yang Mills theory and a type IIB string theory on [itex]AdS_5\times S^5.[/itex] It turned out that this correspondence principle couldn't only be applied to the theories it was originally made for, but also for others, QCD being a famous example: the correspondence offers means to describe quark-gluon plasma. Even though QCD is not conformally invariant, the correspondence still seems to hold in this case. There are also applications in solid state physics: there are holographic descriptions of superconducters and graphene systems.
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