Periodic Reporting for period 2 - GenGeoHol (Non AdS holography and generalized geometric structures)
Reporting period: 2019-03-01 to 2020-08-31
In this ERC project, we propose new technical tools to study how the Holographic Principle can be applied to our Universe and, in particular, to our Cosmology. Because of the expansion of space and time, there is a Cosmological Horizon beyond which we cannot see. It has been proposed that this horizon should also be described within the Holographic approach. In GENGEOHOL we use modern geometric and quantum mechanical techniques to put this problem on equal footing to previously better understood but less realistic models for Holography.
Rather surprisingly, the same techniques that can be used to understand our Cosmology have direct implications for the physics of certain exotic materials that are studied in the lab. These are called ""strongly coupled systems"" and cannot be currently understood by other techniques. In the recent past new phases of matter have been discovered with new exotic symmetries. It is these symmetries that connect these systems through the holographic principle to our previous questions. Therefore, the understanding of space and time can directly lead to progress in more experimentally accessible setups.
Mankind has always wondered about the nature of reality. What is time? How did it begin? How will it end? If we are to answer these questions, we need to first understand what the Holographic Principle has to say about realistic models for space-time. GENGEOHOL is a step in this direction."
First, a proposal was put forward on how to apply the Holographic Principle to Cosmological space-times. The solution proposed within GENGEOHOL is novel in two ways. First, it gives an important role to the observer asking the physical questions. This allows the model to account for time dependent questions which were outside the scope of previous proposals. Second, it embeds Cosmological setups in previous well understood less realistic models. As such, there is great power in this formulation from what has been understood about the Hologrphic Principle in the last twenty years.Besides Cosmological setups, GENGEOHOL has made progress in understanding the Quantum Information aspects of Wormhole geometries.
Second, it was understood how certain generalized geometries are introduced in Holographic setups. This is of great importance as these symmetries connect the study of phases of matter for real physical materials to the question about the individual building blocks of space and time within black holes. A nice application of these ideas was obtained in GENGEOHOL to the physics of superfluids.
Third, it was understood what type of generalized symmetries are responsible for the emergence of General Relativity in Holographic theories. This result is the most concise proof of this phenomenon to this date and provides some perspective on why General Relativity is a preffered theory of gravity.