| This thesis investigates various issues regarding unitarity in the context of Anti-de Sitter/Conformal Field theory (AdS/CFT) dualities. When the boundary duals are conformal, unitarity implies that there are lower bounds on the dimension of primary operators. Now, the AdS/CFT dictionary relates insertions of boundary operators to different choices of boundary conditions on the gravity side. Therefore, we expect the possible choices of boundary conditions in AdS to be restricted accordingly. Our first main goal will be to identify what are the pathologies that occur in the gravitational side of the duality when the boundary operators violate the pertinent unitarity bounds. In all the studied cases, we find that such bulk theories are ill-defined as expected, although unitarity is not nec- essarily violated. As our first example we consider a Klein-Gordon field in AdS, and extend the analysis to bosonic fields of spin 1 and 2 later on, with analogous results. Interestingly, it turns our that the bulk settings are pathological even in the absence of strict conformal invariance. Secondly, we argue that introducing a geometrical cut-off in spacetime along with the appropriate modifications of the boundary conditions yields the resulting (IR) theories well-defined. By study- ing in detail a Klein-Gordon field with boundary conditions that correspond to double-trace deformations, we are able to explicitly verify this claim. Finally, we discuss future research directions which include generalizations of AdS/CFT-like dualities and potential applications for condensed matter theory. |
