The twentieth century saw two mayor revolutions in the area of theoretical physics. The first was the understanding that the force of gravity can be described as a consequence of a geometric description of space and time called General Relativity. The second was the realization that, at the smallest scales, the rules that guide the behavior of subatomic particles are that of quantum mechanics (as opposed to classical mechanics). While these new paradigms have been extremely successful and have been corroborated in experiments at the smallest and largest possible scales they have raised important questions about the nature of reality at the most fundamental level. In particular, these two discoveries, together, have important and puzzling consequences for the basic building blocks of space and time. A window into the nature of this problem is provided by interesting objects called black holes. These are compact astrophysical objects from which light cannot escape. Therefore, we cannot see what happens inside them. But rather surprisingly, General Relativity and Quantum Mechanics put together predict that the degrees of freedom of these objects lie only on their surface and not inside. This became the most important discovery in physics at the end of the twentieth century and goes by the name of the Holographic Principle. It has dominated physics research in the twenty-first century.
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.
A particular direction which has become more important in recent years is the relevance of extended objects in understanding different phases of matter and consistency properties of strongly coupled theories. The presence of extended objects yields generalized notions of symmetry that can be exploited to understand physical phenomena. Furthermore, quantum mechanical objects describing measurements taking place over extended regions of space and time have proven critical in understanding when these theories are consistent and their properties connect to the issue of symmetries mentioned before. Lastly, at the frontier of our understanding, lies the question: what is the relevance of these objects when the theory in question is one when the notions of space and time are dynamical?
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.
