UC Santa Barbara

The planar expansion of large N gauge theories has been a remarkably fruitful idea,inspiring many developments in theoretical physics. Perhaps the most important realization of this idea is the duality between critical string theories in anti de-Sitter spaces and large N conformal field theories, giving a window into otherwise intractable phenomena in quantum field theories. One of the most promising aspects of this duality is the possibility of studying truly quantum aspects of gravitational systems with conventional tools from quantum mechanics. A major obstacle to this endeavor lies in the fact that the most interesting questions about quantum gravity in anti de-Sitter space are related to issues that are beyond current techniques in conformal field theory. This thesis deals with various semiclassical aspects of large operators in holographic conformal field theories, focusing on the study of very large (near-)BPS operators in $\mathcal{N} = 4$ super Yang-Mills theory and their corresponding gravitational avatars.