A study of non-local holography in the AdS/CFT correspondence

This thesis is broadly composed of three topics. After giving a brief overview of the origins of the AdS/CFT duality, we describe a way of representing local bulk fields as quasi-local CFT operators. We show how these smeared boundary operators encode the holographic radial-scale duality, and how this can lead to degrees of freedom consistent with Bekenstein's entropy. We also gain insight into the BTZ black hole, with the horizon, singularity, and thermality arising naturally via these operators.; As another aspect of AdS/CFT, we will be interested in the fate of giant gravitons under a marginal deformation. We review the construction and fluctuation spectrum of giants, and then proceed to evaluate them in two different Penrose limits of Lunin and Maldacena's gamma deformed geometry. We find only one to be stable, and describe how the degeneracy of the spectrum is partially broken.; Finally, we make a first step towards cosmological particle production in string theory by introducing a first quantized alternative approach to the standard method of calculation. We show how the same calculation can be done with Green's Functions---objects which are well defined in a first quantized setting (such as string theory).