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.
