Collapsing Shells in AdS Space and Holographic Thermalization

The AdS/CFT correspondence is the first realization of the holographic principle. The holographic principle makes the bold statement that in a theory of quantum gravity all information in a region of spacetime can be completely described by information on its boundary. This would make the universe in certain sense a hologram, as our spacetime and everything in it could be described by some fundamental degrees of freedom living on the boundary of spacetime. Gauge/gravity dualities realize the holographic principle by stating that string theory in ten-dimensional spacetime and certain gauge field theories living on its boundary can be equivalent descriptions of the same physics. The AdS/CFT correspondence was the first one of these dualities to be discovered. The correspondence equates type IIB string theory on AdS_5× S^5 with \mathcal{N}=4 super Yang-Mills theory living on four-dimensional Minkowski space, which is the boundary of five-dimensional anti-de Sitter space, AdS_5. In this thesis, we first briefly review the necessary theoretical components, which are combined in the correspondence. Then, the AdS/CFT correspondence is motivated by considering the low energy limit of string theory in a spacetime with a stack of coincident D3-branes. The third part of this work is dedicated to the study of the properties and dynamics of the anti-de Sitter bulk. A black hole solution with an asymptotically AdS background is discussed along with its thermodynamics, and the connection with the dual field theory is emphasized. Then we present a model for a collapsing shell in AdS space and solve its dynamics. The black hole state, which the collapsing shell approaches corresponds to thermal equilibrium in the dual field theory. Lastly, we consider our shell model in the context of the AdS/CFT correspondence and present a method for computing two-point correlation functions on the field theory side. This method is then used to compute retarded correlators in a two-dimensional CFT in finite temperature. We are able to reproduce previous results obtained using different computational methods, following a seminal work of Son and Starinets.