@Federico: For references try Gaberdiel's review paper on conformal field theories. For commented pointers to the literature see here ncatlab.org/nlab/show/conformal+field+theory Or for one rigorous definition and derivation of the full theory from the first principles see the book by P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory (Springer, 1997) (and this is my source).

Urs Schreiber, Thanks very much, I am glad for the references.

In my limited experience, I tried to get guided by mathematical naturalness and elegance. All answers were more generally helpful. Thank you for heads up)

Now enroute nevertheless, thanks to the efficiency and generosity of your answers, and remarkably, I learnt a lot. I am beginning to feel like I live in a Seinfeld episode. Though it is a bit embarrassing to have units appearing so prominently in the answers. If the questions fails to be relevant here, I have an excuse.

Thanks Misha for pointing this out. To get a handle of my problem I am trying to wrap the M5's on some manifold, and study the resulting theory. The goal is use AdS/CFT to understand 4d theories that come from wrapping M5's on a Riemann surface. Can wrapped branes preserve SUSY? The embeddings SO(2)→SO(5) is clear. I am trying to find a way to think of this, as the branes wrapping a Riemann surface \Sigma _{g}\subset CY_{3}.