I'm a beginner in learning the AdS/CFT correspondence, and I come across two problems that I hope an answer will be given here.
D branes in string theory are usually introduced through the T-duality of open strings where toroidal compactification of dimension is necessary. However, I think that D branes can live in spacetimes where there is no compactification. Am I right?
I think in the AdS/CFT correspondence, the D branes are placed on the boundary of the AdS spacetime, while the $p$-brane is often said to positioned on the horizon. Is that right? If so, why are the $p$-brane and D brane equivalent?**