Relation between CS/WZW and AdS/CFT

Question

One precise example of realization of the holographic principle is the CS/WZW correspondence, which relates 3d Chern-Simons theory with the 2d Wess-Zumino-Witten model. As explained for example in this article in nlab there is a relation between this correspondence and the AdS3/CFT2 correspondence (which in turn relates 3d gravity and 2d conformal field theory). In particular CS/WZW appears to be some part (nlab says "sector") of the full AdS/CFT correspondence.

How does CS/WZW appear inside AdS3/CFT2? I'm asking, if possible, for a rough explanation of how this works. It seems that this happens in other dimensions too. Is there any similar TFT/CFT correspondence that can be seen as a sector of the usual AdS/CFT setting with $\rm{AdS}_5\times S^5$ type II supergravity / 4d $\mathcal{N}=4$ super Yang-Mills?

This post imported from StackExchange Physics at 2017-02-18 11:05 (UTC), posted by SE-user coconut

Answer 1

Holographic duality doesn't necessarily require $AdS$ space. See, for example, the famous CS/Topological String duality. In particular, I don't think that it is possible to consider CS/WZW as $AdS_3/CFT_2$.

This post imported from StackExchange Physics at 2017-02-18 11:05 (UTC), posted by SE-user Andrey Feldman

Comments

I'm aware that there are holographic dualities that don't involve AdS. CS/WZW is one example. However, it seems that AdS3/CFT2 has some sector that can be identified with CS/WZW (see the link in my question). Notice that I'm not saying that those two dualities are the same, but that there is some relatiom between them.

This post imported from StackExchange Physics at 2017-02-18 11:05 (UTC), posted by SE-user coconut