Quantum Gravity and the Holographic Principle

TL;DR

This thesis explores two holographic approaches to quantum gravity: a topological field theory analysis in high-energy regimes and the AdS/CFT correspondence for reconstructing bulk spacetime from boundary data.

Contribution

It provides new insights into the topological nature of quantum gravity in high-energy limits and develops explicit holographic reconstruction techniques for bulk metrics from boundary conformal field theories.

Findings

Quantum gravity in high-energy regimes is topological for asymptotically dS and AdS geometries.

Explicit formulas for holographic stress-energy tensors are derived.

Analysis of warped compactifications and extra-dimensional information retrieval.

Abstract

In this thesis we study two different approaches to holography, and comment on the possible relation between them. The first approach is an analysis of the high-energy regime of quantum gravity in the eikonal approximation, where the theory reduces to a topological field theory. This is the regime where particles interact at high energies but with small momentum transfer. We do this for the cases of asymptotically dS and AdS geometries and find that in both cases the theory is topological. We discuss the relation of our solutions in AdS to those of Horowitz and Itzhaki. We also consider quantum gravity away from the extreme eikonal limit and explain the sense in which the covariance of the theory is equivalent to taking into account transfer of momentum. The second approach we pursue is the AdS/CFT correspondence. We provide a holographic reconstruction of the bulk space-time metric and of bulk fields on this space-time, out of conformal field theory data. Knowing which sources are turned on is sufficient in order to obtain an asymptotic expansion of the bulk metric and of bulk fields near the boundary to high enough order so that all infrared divergences of the on-shell action are obtained. We provide explicit formulae for the holographic stress-energy tensors associated with an arbitrary asymptotically AdS geometry. We also study warped compactifications, where our d-dimensional world is regarded as a slice of a (d+1)-dimensional space-time, and analyse in detail the question as to where the d-dimensional observer can find the information about the extra dimension.