Boundary conditions in asymptotically anti-de Sitter spacetime and the Anti-de Sitter/Conformal Field Theory correspondence

The properties of asymptotically anti-de Sitter spacetimes have been of much recent interest in light of a remarkable conjecture known as the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. In this dissertation, we study general boundary conditions for various matter fields in asymptotically AdS spacetime, and discuss the implications of our results in the context of AdS/CFT. We begin by considering tachyonic scalar fields coupled to gravity in the so-called "designer-gravity" theories. We construct the Hamiltonian generators of asymptotic symmetries for such systems using the covariant phase space method and show that these charges are finite. Using a Witten-Nester style proof, we obtain a positive energy theorem under the conditions that the function W specifying the boundary conditions has a global minimum and that the scalar potential admits an appropriate superpotential. We then investigate boundary conditions for massive spin-1/2 fermions in exact AdS, and find that (as with scalars) for a special mass range there is a choice of boundary conditions at infinity. Using these results, we identify boundary conditions for combined scalar/fermion systems that preserve N = 1 supersymmetry on the boundary. Finally, we demonstrate similar results for spin-3/2 fields and further show that more general boundary conditions are allowed for any mass if one appropriately "renormalizes" the inner product. We then investigate supersymmetric boundary conditions for d = 4, N = 1 AdS supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We argue that the dual of such a theory is a 3-dimensional supergravity theory.