Periodic Reporting for period 4 - Emergent-BH (Emergent spacetime and maximally spinning black holes)
Okres sprawozdawczy: 2021-03-01 do 2022-08-31
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.
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.
Some of the central results of this project have been to put forth the first concrete example of a (class of) dipole CFTs in two dimensions, which moreover turn out to be entirely solvable. After exploring some of the basic properties of these theories, we set up a program to understand their symmetries. These turned out to be infinite in number and organised precisely into a Virasoro algebra. We understood concretely the mechanism through which this novel type of Virasoro symmetry is reconciled with the non-locality of the theory. Thus, the picture suggested by the study of maximally spinning black holes was entirely correct, and this new type of symmetries do, indeed, exist!
In standard, local CFTs, the Virasoro symmetry is extremely powerful in constraining physical observables. We showed the same is true for the two-dimensional dipole CFTs we studied; in particular, low-point correlation functions of appropriately defined operators are entirely fixed. Remarkably, the form of these correlators precisely reproduces the form of scattering data in the near-horizon of a maximally spinning black hole!
Our subsequent goal was to understand how spacetime emerges from these dipole CFTs. We were able to find the precise holographic map between the field theory and gravity and find some novel effects in the way spacetime emerges from field theory .
The ideas and techniques that we developed for the study of two-dimensional dipole CFTs turned out to be very relevant for the study of a different class of exactly solvable irrelevant deformations, known as TT deformations. Even though they are structurally similar to dipole CFTs, these theories have rather different applications, such as to understanding flux tubes in quantum chromodynamics (a.k.a. QCD - the theory of strong interactions, which hold together the atomic nuclei), but also to understanding holography in asymptotically flat spacetimes and near the horizon of general black holes. We showed that these non-local theories, too, possess Virasoro symmetry and we developed precision holography also in their case.
Thus, the dipole CFTs that we had uncovered by studying maximally spinning black holes are a subset of a much larger class of “non-local CFTs”, whose general properties we are setting out to uncover. This new class of theories is likely to open up a new window into flat holography – the holographic duality that describes our universe at sub-Hubble scales – from a vantage point that is entirely different from current ways to approach this important subject. Going beyond holography on faraway skies, one may naturally wonder whether the novel symmetries we have uncovered through this project could be seen in systems closer to our reach, such as quantum chromodynamics or in some exotic phase transitions.
The results of this work have been disseminated at many international conferences for specialists in the field; a popular description can be found at https://news.universite-paris-saclay.fr/en/news/emergence-gravity-and-black-holes
In standard, local CFTs, the Virasoro symmetry is extremely powerful in constraining physical observables. We showed the same is true for the two-dimensional dipole CFTs we studied; in particular, low-point correlation functions of appropriately defined operators are entirely fixed. Remarkably, the form of these correlators precisely reproduces the form of scattering data in the near-horizon of a maximally spinning black hole!
Our subsequent goal was to understand how spacetime emerges from these dipole CFTs. We were able to find the precise holographic map between the field theory and gravity and find some novel effects in the way spacetime emerges from field theory .
The ideas and techniques that we developed for the study of two-dimensional dipole CFTs turned out to be very relevant for the study of a different class of exactly solvable irrelevant deformations, known as TT deformations. Even though they are structurally similar to dipole CFTs, these theories have rather different applications, such as to understanding flux tubes in quantum chromodynamics (a.k.a. QCD - the theory of strong interactions, which hold together the atomic nuclei), but also to understanding holography in asymptotically flat spacetimes and near the horizon of general black holes. We showed that these non-local theories, too, possess Virasoro symmetry and we developed precision holography also in their case.
Thus, the dipole CFTs that we had uncovered by studying maximally spinning black holes are a subset of a much larger class of “non-local CFTs”, whose general properties we are setting out to uncover. This new class of theories is likely to open up a new window into flat holography – the holographic duality that describes our universe at sub-Hubble scales – from a vantage point that is entirely different from current ways to approach this important subject. Going beyond holography on faraway skies, one may naturally wonder whether the novel symmetries we have uncovered through this project could be seen in systems closer to our reach, such as quantum chromodynamics or in some exotic phase transitions.
The results of this work have been disseminated at many international conferences for specialists in the field; a popular description can be found at https://news.universite-paris-saclay.fr/en/news/emergence-gravity-and-black-holes