Aspects of holography

The principle of holography---that theories of gravity should be described in terms of their boundaries---has been the driving force behind many great strides in quantum gravity, gauge theory, and even in phenomenology. The most concrete example of holographic duality is the AdS/CFT correspondence, which relates quantum gravity in Anti-deSitter space to a Conformal Field Theory in Minkowski space. In this thesis we begin with a chapter on black holes in the AdS/CFT duality, and then move on to the main line of development, where we describe the exciting first steps towards the discovery of a holographic duality for quantum gravity in flat spacetime.;A holographic description of flat spacetime would be a theory of the Scattering Matrix, which contains the quantum mechanical amplitudes that determine how incoming states from past infinity scatter into outgoing states at future infinity. We suspect that a holographic duality between a local spacetime description of quantum gravity and a non-local boundary description of the S-Matrix would be a weak coupling-weak coupling duality. We work towards this concrete goal from the bottom up by studying new methods for computing scattering amplitudes.;We begin by studying the BCFW Recursion Relations, which are an explicitly non-local, boundary oriented method for computing tree-level scattering amplitudes. We give an elementary derivation of these relations for general theories in any number of dimensions, showing that their existence is a deep feature of field theory. Next we argue that, counter to naive expectations, N = 8 Supergravity may be the simplest quantum field theory. We demonstrate this by explicitly solving its one-loop S-Matrix with techniques that rely on our understanding of tree amplitudes to vastly simplify calculations. Finally, we show that the BCFW recursion relations find their natural home in Twistor Space, where it is possible to formulate classical scattering theory in a beautiful and manifestly holographic way. This investigation takes us beyond the BCFW relations; it suggests that scattering amplitudes can be calculated in terms of holographic "words" whose "grammar" has yet to be uncovered.