Periodic Reporting for period 1 - BHHQG (Black Hole Horizons in Quantum Gravity)
Berichtszeitraum: 2022-09-01 bis 2025-02-28
The project "Black Hole Horizons in Quantum Gravity" aims for an in-depth investigation of black holes and the information paradox in the context of quantum gravity. Due to the recent breakthroughs in astronomy, these exotic objects have moved from the purely theoretical realm to being abundant in our physical universe. Surprisingly, our theoretical understanding of them is insufficient to even in principle understand their horizons and what happens behind them. Our approach to tackle these questions is to combine a lower-dimensional approach with holography as a guide. Within this framework, substantial breakthroughs were made in the Sachdev-Ye-Kitaev models, and their low-energy gravitational description in terms of Jackiw-Teitelboim gravity. This model is exactly solvable to a large degree, and many important lessons on black hole physics and quantum gravity can be studied quantitatively and exactly.
Our goals within this project span across two lines.
Firstly, we will apply quantum gravitational results on the Jackiw-Teitelboim gravity model to address aspects of the black hole information puzzle in a quantitative way and probe the deep questions on black hole horizons largely building on our detailed knowledge of this model. In particular, we will calculate correlation functions of local infalling bulk observables, and assess the effect of quantum gravitational corrections to evaporation. Secondly, it is vital to investigate the universality of the set of techniques and methods we use in Jackiw-Teitelboim gravity. We will do this by pursuing several roads simultaneously (dilaton gravity models, 2d string theory, the original Sachdev-Ye-Kitaev model, supersymmetric models and 3d pure gravity). Armed with these results, we will extrapolate to higher dimension and in particular to our physical universe making contact with the first objective.
Our goals within this project span across two lines.
Firstly, we will apply quantum gravitational results on the Jackiw-Teitelboim gravity model to address aspects of the black hole information puzzle in a quantitative way and probe the deep questions on black hole horizons largely building on our detailed knowledge of this model. In particular, we will calculate correlation functions of local infalling bulk observables, and assess the effect of quantum gravitational corrections to evaporation. Secondly, it is vital to investigate the universality of the set of techniques and methods we use in Jackiw-Teitelboim gravity. We will do this by pursuing several roads simultaneously (dilaton gravity models, 2d string theory, the original Sachdev-Ye-Kitaev model, supersymmetric models and 3d pure gravity). Armed with these results, we will extrapolate to higher dimension and in particular to our physical universe making contact with the first objective.
Since starting the project on 1/9/2022, we have made progress on most work packages of the project.
At the very start of the project, we analyzed how JT gravity black hole models need to be adjusted to incorporate additional conserved charges in the framework. In particular, we constructed and solved dissipative equations of motion describing the combined energy+charge dissipation. This lead to interesting semi-classical solutions that exhibit superradiance properties of black hole evaporation. We applied the results of this system also as an example of a different “operational” definition of an entanglement island in a black hole geometry, where the location of the island itself is operationally defined by an observer, allowing us to embed the older concept of “renormalized entanglement entropy” into this framework. These results have been published. More ideas are being investigated at the moment by various team members. One of the team members has investigated near-horizon near-extremal dynamics of higher-dimensional black holes in a cosmological (de Sitter) context, and published these findings.
We have recently made substantial progress in understanding a particular scaling limit of the SYK model, where the number of fermions goes to infinity and the number of fermions involved in each interaction as well, keeping their ratio (suitably defined) fixed as one takes the limit. This double-scaled SYK (or DSSYK) model has been attracting substantial attention in the field the past few years. The reason for this attention is that this is a microscopic (UV-complete) model that has several features to it that are very hard to explain within the usual holographic gravitational framework (such as a bounded energy spectrum).
Our group has been developing group-theoretical techniques to analyze these lower-dimensional models for several years, and we have recently applied these methods to the DSSYK model itself, allowing us to obtain substantial insight into the structural aspects of these models, and how they interrelate. Following this methodology, we have been able to propose various novel and important results such as:
1. A q-deformation of the boundary Schwarzian model,
2. A proposal for a bulk holographic dual of the DSSYK model.
We are at the moment pursuing this research line further with various collaborators. In particular, with two local PhD students, we are currently working out various representation-theoretic properties of these models and how they differ from more established models (such as Liouville gravity or the minimal string).
We have also made substantial progress on generalizing and deriving exact results for gravity models that have more supersymmetry. We have published two research papers on this topic at the time of writing, providing in-depth investigations of the N=2 JT supergravity models from our group-theoretic perspective. We have in particular also derived various N=1,2,4 results in a simple and efficient way using our techniques, that were only partly known in the literature. This serves as an illustration of the strength of our unifying framework and methodologies.
We have also applied our methods to 2+1 dimensional gravity, elucidating a similar structure of the correlation functions as in the 1+1 dimensional models. This has allowed us to formulate and postulate a generic statement on how all of these models would factorize across bulk entangling surfaces: it is the co-product of the associated Hopf algebra. This requires the introduction of boundary (“edge”) degrees of freedom that have been studied and known for a long time, but now constructed within our unified framework. Moreover, applying this to 2+1d gravity, this allowed us to consider gravitational counterparts of anyonic degrees of freedom at the black hole horizon. These results have been published.
At the very start of the project, we analyzed how JT gravity black hole models need to be adjusted to incorporate additional conserved charges in the framework. In particular, we constructed and solved dissipative equations of motion describing the combined energy+charge dissipation. This lead to interesting semi-classical solutions that exhibit superradiance properties of black hole evaporation. We applied the results of this system also as an example of a different “operational” definition of an entanglement island in a black hole geometry, where the location of the island itself is operationally defined by an observer, allowing us to embed the older concept of “renormalized entanglement entropy” into this framework. These results have been published. More ideas are being investigated at the moment by various team members. One of the team members has investigated near-horizon near-extremal dynamics of higher-dimensional black holes in a cosmological (de Sitter) context, and published these findings.
We have recently made substantial progress in understanding a particular scaling limit of the SYK model, where the number of fermions goes to infinity and the number of fermions involved in each interaction as well, keeping their ratio (suitably defined) fixed as one takes the limit. This double-scaled SYK (or DSSYK) model has been attracting substantial attention in the field the past few years. The reason for this attention is that this is a microscopic (UV-complete) model that has several features to it that are very hard to explain within the usual holographic gravitational framework (such as a bounded energy spectrum).
Our group has been developing group-theoretical techniques to analyze these lower-dimensional models for several years, and we have recently applied these methods to the DSSYK model itself, allowing us to obtain substantial insight into the structural aspects of these models, and how they interrelate. Following this methodology, we have been able to propose various novel and important results such as:
1. A q-deformation of the boundary Schwarzian model,
2. A proposal for a bulk holographic dual of the DSSYK model.
We are at the moment pursuing this research line further with various collaborators. In particular, with two local PhD students, we are currently working out various representation-theoretic properties of these models and how they differ from more established models (such as Liouville gravity or the minimal string).
We have also made substantial progress on generalizing and deriving exact results for gravity models that have more supersymmetry. We have published two research papers on this topic at the time of writing, providing in-depth investigations of the N=2 JT supergravity models from our group-theoretic perspective. We have in particular also derived various N=1,2,4 results in a simple and efficient way using our techniques, that were only partly known in the literature. This serves as an illustration of the strength of our unifying framework and methodologies.
We have also applied our methods to 2+1 dimensional gravity, elucidating a similar structure of the correlation functions as in the 1+1 dimensional models. This has allowed us to formulate and postulate a generic statement on how all of these models would factorize across bulk entangling surfaces: it is the co-product of the associated Hopf algebra. This requires the introduction of boundary (“edge”) degrees of freedom that have been studied and known for a long time, but now constructed within our unified framework. Moreover, applying this to 2+1d gravity, this allowed us to consider gravitational counterparts of anyonic degrees of freedom at the black hole horizon. These results have been published.
Our methodology relies very heavily on utilizing group-theoretic techniques to the various physical models (JT gravity, its supersymmetric cousings, Liouville gravity, the minimal string, and the DSSYK model) and unifying them in this language. This methodology has been partially developed before the start of this project, but it has been worked out in much more detail in the past few years during this project. This has allowed us to make physical proposals that would be harder to make from other perspectives, illustrating the potential of this approach. We have used these methods in particular to give detailed bulk holographic proposals for the DSSYK model, and to derive expressions for so-called end-of-the-world brane amplitudes in various gravitational models (of interest in the current community) in a conceptually unified and direct way. In particular, some of our results on supersymmetric JT gravity models have also highlighted that our approach requires some novel mathematical objects, which we derived as well. This research line hence interplays quite nicely with more abstract mathematical representation theory, and in particular focuses on how such results are then utilized in concrete gravitational physical systems. The recent results we have obtained on the double-scaled SYK model itself I would consider a signficant development we have achieved in the field. In particular how our group-theoretic approach led us to a proposal for a holographic bulk dual description as a dilaton gravity model with a sine potential, and a deformed version of the boundary Schwarzian action (which we dubbed “q-Schwarzian”).