# Why do we say that AdS/CFT is a background independent definition of string theory?

It is usually said that AdS/CFT is a background independent definition of string theory, how this concept emerge from the AdS/CFT correspondence?

We can define string theory on other manifolds beside those which are related to AdS/CFT paradigm.

Thanks

• Could you provide some references for this claim? I have heard it also and would like to read more about it. – pathintegral Mar 21 at 19:14
• @pathintegral Polchinski and Horowitz have discussed about it in the book by Daniele Oriti "approachs to quantum gravity" part 2 chapter 10, but it is not too detailed. – Arian Mar 21 at 21:43

• @pathintegral The background is "flat target space". We really only can do the ordinary string path integral/sum over worldsheets when the target space (in the viewpoint of string theory being a $\sigma$-model) is flat. When the target space is curved with an aribtrary metric $G_{\mu\nu}$, the only known way to deal with it is to split it as $\eta_{\mu\nu} + \chi_{\mu\nu}$ and recognize the $+\chi_{\mu\nu}$ term inside the path integral as being the same as the insertion of a graviton vertex operator. The $\eta$ is the flat Minkowski metric and it is the "background" meant here. – ACuriousMind Mar 21 at 19:28
• @Arian You seem to be misunderstanding what "background" means. Yes, AdS/CFT only works for string theories whose target space is AdS. But that has nothing to do with a "background", it's just a subset of string theories. "background independence" w.r.t. to the metric means that we are able to describe the theory on a target space with metric $G_{\mu\nu}$ without having to split it into the Minkowski metric and a perturbation around it, see my first comment. – ACuriousMind Mar 22 at 19:37