Cobordism Conjecture in AdS

McNamara and Vafa conjectured that any pair of consistent quantum gravity theories can be connected by a domain wall. We test the conjecture in the context of the AdS/CFT correspondence. There are topological constraints on existence of an interface between the corresponding conformal field theories. We discuss how to construct domain walls in AdS predicted by the conjecture when the corresponding conformal interfaces are prohibited by topological obstructions.