Black holes are fascinating objects. The extreme violence of a star’s collapse, the strength of the tidal forces, the formation of a surface - the horizon - of no return, are certainly powerful images. But even from a theoretical point of view, black holes are very striking. To make thermodynamics compatible with the fact that matter can fall into a black hole, the latter needs to be assigned an immense entropy, proportional to the area of its horizon. Moreover, Stephen Hawking showed that, quantum-mechanically, black holes evaporate, emitting thermal radiation. This appears to lead to violations of quantum mechanics, the main pillar of our understanding of microscopic physics. Thus, black holes reveal a powerful tension between general relativity and quantum mechanics, known as the black hole information paradox.
The fact that the black hole entropy scales as an area, rather than a volume has lead t’Hooft to propose that quantum gravity is “holographic”, i.e. gravitational physics in a given region of space-time can be entirely encoded in a non-gravitational theory - a “field theory” - residing at the boundary of that region- just like in a hologram, where a three-dimensional image can be fully reconstructed from data on a two-dimensional surface. As in the hologram, the dictionary between gravity and the boundary field theory is very complicated, and one can think of gravity and the extra dimension it occupies as “emergent”. Thus, in holography, space is not a fundamental concept. This also has profound implications for our own universe, where it appears that time itself is the emergent direction. Holography can resolve the tension between gravity and quantum mechanics through subtle non-local effects (i.e. which connect distant points in spacetime).
There has been significant progress in understanding the emergence mechanism in certain special contexts such as gravity in hyperbolic spacetimes, which occur frequently in the context of string theory. However, very little is known about it for the spacetime backgrounds relevant to the real world, due mainly to our lack of knowledge of the underlying field theories, for which a completely new framework needs to be developed.
The goal of this project was to uncover the fundamental nature of spacetime and gravity in our own universe by: i) formulating and working out the properties of the relevant lower-dimensional field theories and ii) studying the mechanism by which spacetime and gravity emerge from them. The main idea was to address these problems not in the most general cosmological setting - which is conceptually hard- but by concentrating on the near-horizon regions of maximally spinning black holes, for which the dual field theories greatly simplify and correspond to certain non-local (the technical term is “irrelevant”) deformations of two-dimensional conformal field theories (CFTs) - a class of quantum theories that is extremely well-studied and that is relevant to many different areas of physics, from phase transitions to string theory.
These non-locally - deformed theories, termed “dipole CFTs”, were conjectured to exist based on evidence coming from string theory but, at the start of this research project, no concrete example of a two-dimensional “dipole CFT” was known. Moreover, the study of the dual maximally spinning black hole backgrounds suggested these theories had rather unusual properties, such as the presence of an infinite-dimensional “Virasoro” symmetry, despite their explicit non-locality. Or, Virasoro symmetry is the hallmark of the well-studied local two-dimensional CFTs, and its potential presence in a non-local theory appeared rather puzzling.
