Periodic Reporting for period 2 - HoloFlat (Holography for Asymptotically Flat Spacetimes)
Periodo di rendicontazione: 2021-10-01 al 2022-09-30
Over the last 25 years, there has been immense progress in understanding the elusive nature of quantum gravity and black holes by using the so-called holographic principle. This principle states that a theory of quantum gravity in a given region of spacetime can be equivalently described in terms of a quantum field theory encoded at the boundary of said region. This duality allows one to translate very complicated problems into accessible ones and provides a sneak peek at the principles a consistent theory of quantum gravity should obey. However, until now, most holographic applications only apply to specific situations. In particular, holographic applications to realistic spacetimes, such as the ones we live in, have not been developed yet. Most spacetimes relevant for astrophysical purposes are characterized by having a vanishing cosmological constant or phrased more geometrically; they are asymptotically flat, in a very similar sense as a sheet of paper is flat.
The main objective of this project is to establish a fundamental understanding of quantum gravity for asymptotically flat spacetimes by developing novel holographic tools. This will be done first in a simplified setup where one has a very high degree of control and then extended to more realistic setups. The long-term goal of HoloFlat is to apply these tools to astrophysical black holes to gain a deeper understanding of these objects at a quantum level.
Right now is a fascinating time to study quantum gravity and black holes. Thanks to the overwhelming evidence provided by LIGO gravitational wave observatory and the genuine black hole images the Event Horizon Telescope has provided us, we now also have access to a wealth of experimental data that can be used to test theoretical predictions about quantum gravity via black holes. The importance of this project is rooted in its profound implications for our understanding of quantum gravity and black hole physics. Furthermore, the holographic principle is an inherently interdisciplinary field of research, and discoveries regarding the holographic nature of quantum gravity in asymptotically flat spacetimes will unveil novel connections between previously disconnected research fields.
The conclusions of this Marie Skłodowska-Curie Action are:
1) The infinite-dimensional symmetries at the boundary of asymptotically flat spacetimes give rise to a novel kind of quantum field theory that provides fundamental insights into quantum gravity.
2) There is an intimate connection between quantum information and geometry that also extends to asymptotically flat spacetimes.
3) A thorough understanding of the dual quantum field theories is key to revealing the holographic properties of black holes.
The main objective of this project is to establish a fundamental understanding of quantum gravity for asymptotically flat spacetimes by developing novel holographic tools. This will be done first in a simplified setup where one has a very high degree of control and then extended to more realistic setups. The long-term goal of HoloFlat is to apply these tools to astrophysical black holes to gain a deeper understanding of these objects at a quantum level.
Right now is a fascinating time to study quantum gravity and black holes. Thanks to the overwhelming evidence provided by LIGO gravitational wave observatory and the genuine black hole images the Event Horizon Telescope has provided us, we now also have access to a wealth of experimental data that can be used to test theoretical predictions about quantum gravity via black holes. The importance of this project is rooted in its profound implications for our understanding of quantum gravity and black hole physics. Furthermore, the holographic principle is an inherently interdisciplinary field of research, and discoveries regarding the holographic nature of quantum gravity in asymptotically flat spacetimes will unveil novel connections between previously disconnected research fields.
The conclusions of this Marie Skłodowska-Curie Action are:
1) The infinite-dimensional symmetries at the boundary of asymptotically flat spacetimes give rise to a novel kind of quantum field theory that provides fundamental insights into quantum gravity.
2) There is an intimate connection between quantum information and geometry that also extends to asymptotically flat spacetimes.
3) A thorough understanding of the dual quantum field theories is key to revealing the holographic properties of black holes.
In this project, we investigated quantum gravity with a vanishing cosmological constant. We developed several novel holographic tools that provide unique insights into holography in asymptotically flat spacetimes with a particular focus on three spacetime dimensions. This includes an explicit example of a (partial) candidate for the dual quantum field theory for flat space quantum gravity in three dimensions, successfully coupling a scalar field to (higher-spin) gravity in flat space, the first (holographic) example of quantum chaos in a non-relativistic quantum field theory, and constrained the space of possible dual quantum field theories for asymptotically flat spacetimes with additional symmetries.
We performed a Hamiltonian reduction of the Einstein-Hilbert action in three spacetime dimensions. We showed that the resulting action at null infinity (one of the boundaries of asymptotically flat spacetime) is given by the geometric action on Bondi-van der Burg-Metzner-Sachs (BMS) coadjoint orbits. This provided an explicit example of a quantum field theory dual to asymptotically flat spacetime. Using this action, we computed quantum corrections to various quantities, such as the entanglement entropy of a bipartite system in the dual quantum field theory, the partition function, and BMS conformal blocks. Furthermore, we also developed a new formalism that allows one to couple matter fields to a very general flat background metric (including higher-spin symmetries). This also required introducing a completely novel (infinite-dimensional) symmetry algebra that is interesting to study even beyond the scope of this particular project. To elucidate the intricate connection between quantum information and geometry, we computed out-of-time-ordered correlation functions in Galilean and Carrollean quantum field theories and studied quantum chaos. By doing so, we were also able to show that the spatial distance between two different observers in a toy model of an expanding universe also shows chaotic behavior in the presence of a gravitational shockwave. During the final stages of this project, we focused on further restricting the space of possible dual quantum field theories for asymptotically flat spacetimes with additional (u(1)) symmetries by computing three-point coefficients. We could also provide a holographic interpretation in terms of charged scalar field in the presence of a cosmological horizon.
In addition, the researcher also published an article in a journal aimed at a general physics-interested audience, explaining particular aspects of his research on quantum gravity and flat space holography.
All results of this action were disseminated via publication in peer-reviewed international scientific journals and, at the same time, uploaded as pre-prints on arXiv.org to make sure that the public can openly access all results. Furthermore, the researcher participated in various dissemination activities such as e.g. conferences or public presentations to communicate his results to both a specialist and a general physics-interested audience.
We performed a Hamiltonian reduction of the Einstein-Hilbert action in three spacetime dimensions. We showed that the resulting action at null infinity (one of the boundaries of asymptotically flat spacetime) is given by the geometric action on Bondi-van der Burg-Metzner-Sachs (BMS) coadjoint orbits. This provided an explicit example of a quantum field theory dual to asymptotically flat spacetime. Using this action, we computed quantum corrections to various quantities, such as the entanglement entropy of a bipartite system in the dual quantum field theory, the partition function, and BMS conformal blocks. Furthermore, we also developed a new formalism that allows one to couple matter fields to a very general flat background metric (including higher-spin symmetries). This also required introducing a completely novel (infinite-dimensional) symmetry algebra that is interesting to study even beyond the scope of this particular project. To elucidate the intricate connection between quantum information and geometry, we computed out-of-time-ordered correlation functions in Galilean and Carrollean quantum field theories and studied quantum chaos. By doing so, we were also able to show that the spatial distance between two different observers in a toy model of an expanding universe also shows chaotic behavior in the presence of a gravitational shockwave. During the final stages of this project, we focused on further restricting the space of possible dual quantum field theories for asymptotically flat spacetimes with additional (u(1)) symmetries by computing three-point coefficients. We could also provide a holographic interpretation in terms of charged scalar field in the presence of a cosmological horizon.
In addition, the researcher also published an article in a journal aimed at a general physics-interested audience, explaining particular aspects of his research on quantum gravity and flat space holography.
All results of this action were disseminated via publication in peer-reviewed international scientific journals and, at the same time, uploaded as pre-prints on arXiv.org to make sure that the public can openly access all results. Furthermore, the researcher participated in various dissemination activities such as e.g. conferences or public presentations to communicate his results to both a specialist and a general physics-interested audience.
The holographic principle has been intensely studied involving spacetimes with a negative cosmological constant. However, a complete holographic description for more realistic spacetimes is still missing. This research project has made significant contributions towards closing this gap by developing a holographic correspondence for spacetimes with vanishing cosmological constant, which is highly relevant for most astrophysical purposes.
In this MSC action, we developed novel tools and performed various non-trivial checks of a putative holographic correspondence in spacetimes with a vanishing cosmological constant that were previously impossible. The approach taken in this action was to focus on a simplified setup that allows for a very high degree of control and addresses essential fundamental questions. By doing so, we were able to identify a candidate for a dual quantum field theory, make predictions for quantum corrections to general relativity and develop novel mathematical structures that are expected to find applications also in other fields of physics and mathematics.
Since most of this action is based on symmetries and universal properties of gravity and the involved quantum field theories, the results of this action will also be of interest far beyond the time frame of this project. This MSC action has yielded new insights into fundamental aspects of the holographic principle and thus significantly contributed to a deeper understanding of quantum gravity in asymptotically flat spacetimes.
In this MSC action, we developed novel tools and performed various non-trivial checks of a putative holographic correspondence in spacetimes with a vanishing cosmological constant that were previously impossible. The approach taken in this action was to focus on a simplified setup that allows for a very high degree of control and addresses essential fundamental questions. By doing so, we were able to identify a candidate for a dual quantum field theory, make predictions for quantum corrections to general relativity and develop novel mathematical structures that are expected to find applications also in other fields of physics and mathematics.
Since most of this action is based on symmetries and universal properties of gravity and the involved quantum field theories, the results of this action will also be of interest far beyond the time frame of this project. This MSC action has yielded new insights into fundamental aspects of the holographic principle and thus significantly contributed to a deeper understanding of quantum gravity in asymptotically flat spacetimes.