What We Have Learned of Quantum Gravity From Holography

Abstract

The existence of a correspondence between quantum and gravitational theories has been conjectured for a long time. The conjecture began with Super Yang Mills gauge theories as the quantum theories, and D-P branes string theories as the gravitational theories. Since then, the conjecture has developed greatly. The aim of this dissertation is to explore this development. To do this, we first start by setting some background information regarding the holographic principal and quantum gravitational theories followed by a brief black holes thermodynamics review. We then start by explaining the gauge/gravity duality followed by a journey through the various models ranging from the very first proposed model of the conjecture (BFSS) and going through much later developed models like BMN. We then see the conjecture being evolved to the point where the quantum theories are ungauged. Ending with the simplest model to date, in which the quantum theory is a simple quantum mechanical system and the gravitational theory is a black hole. We then see the important role to be played by quantum simulation in order to advance this field of literature further.