I want to apply for a PhD program (a direct PhD since I already have a master's degree). I am interested in the AdS/CFT correspondence which I currently only qualitatively know about. I have a couple of questions:
1) I was looking for a prospective advisor who is doing either numerical or analytical calculations on the weakly coupled theory and trying to understand the strongly coupled dual theory. This I think will help me understand the correspondence a bit better. However, I also see that some professors are working on integrability from the perspective of AdS/CFT. In my (somewhat naive) point of view, I don't see integrability as inherently connected to AdS/CFT because, for example, one can apply integrability to, say, N=4 super Yang-Mills theory even when it is strongly coupled without making any reference to its gravity dual or to the AdS/CFT correspondence. Does anyone know if working in integrability would help me get acquainted with how the AdS/CFT correspondence works?
2) If I do integrability during the PhD, how easy/difficult would it be to switch over to, say, numerical calulations like the one mentioned in point 1), when I apply for a post-doc if I feel it is the right move later on?