1) In AdS/CFT, what does a different CFT mean in gravity? 2) Also, if the background metric is curved in CFT, how does it appear in the corresponding gravity side?
In the gauge/gravity duality (a.k.a. AdS/CFT), a gravity theory, in which the gravity as a dynamical field, with an asymptotically AdS boundary is related to a conformal field theory with the topology of the AdS boundary. In this correspondence, different states in CFT corresponds to a different geometry in the gravity side. 1) But CFT is not one particular QFT (There are many other gauge theories not N=4 super Yang-Mills, aren’t there?). Then how is the string theory in asymptotically AdS deformed by considering other gauge theories apart from N=4 SYM? 2) We might consider “gravity” (I mean the metric) taken into account in gauge theory? i.e. CFT on curved spacetime background