The holographic principle in quantum gravity - Arifa, Khatee Zathul (2019)
The Holographic Principle conjectures that all information contained within the bulk of spacetime is encoded in its boundary. AdS/CFT is a manifestation of this theory, and it provides a map between a quantum theory of gravity and a non-gravitational quantum field theory. This principle is currently being investigated as it could potentially be the postulate that guides in formulating quantum gravitational theories. In this project, we explored some important aspects of the holographic principle by studying a particular example of the AdS3/CFT2 correspondence, where the 2 dimensional CFT theory is taken to be living on the boundary of AdS3. We then derived some important properties that the CFT2 theory should have to correctly reproduce the same results as quantum gravity in AdS3 spacetime. Most importantly, we computed the central charge, which is an intrinsic quantity pertaining to CFT, by comparing the trace anomalies that arose from the stress tensors of CFT2 and AdS3 at its boundary. This is an important quantity that will help in matching gravitational descriptions to the quantum field theory counterparts, such as recovering the Bekenstein-Hawking black hole entropy from the CFT2's Cardy Formula. Lastly, we studied scalar propagators on BTZ black hole spacetime and matched them to the CFT2 two-point functions, which has a periodicity that captures the Hawking Temperature of the BTZ black hole.