## Final Report Summary - QUNAT (Quantum Mechanical Nature of Black Holes)

The three most important results of the QUNAT project are:

1) That it was understood how to describe the so-called D-branes using Spin Matrix Theory. D-branes are non-perturbative objects just like black holes, so understand D-branes is a very good step on to understanding black holes. This work was done in Phys. Rev. D 94, no. 6, 066001. It revealed how D-branes, that are described classically in a gravitational background, emergence from a quantum theory, including their interactions. The importance of their interactions is that this allowed for the first time to go beyond the supersymmetric limit of D-branes, since the interactions introduce non-supersymmetric corrections.

2) That a new type of geometry that emerges from Spin Matrix theory has been discovered. This work was done by the researcher with Niels Obers and Jelle Hartong that will be published in Phys. Rev. D. Part of understanding black holes is to understand how geometry emerges from a quantum theory. In this case we are able to understand the emergence of geometry from all Spin Matrix theories. This shows in particular that the emergent geometry is a new type of geometry that has not been considered before.

3) That one can make quantitative description of the thermodynamics of string theory emerging from a holographically dual gauge theory. This work was done by the researcher with Matthias Wilhelm and is expected to be published in Physical Review Letters. This is an important step in describing the thermodynamics of black holes, which are part of string theory, from point of view of a dual quantum theory without gravity. In particular, the thermodynamic phase transition temperature that is described quantitatively in this work is connected to the phase transition to a black hole.

In a broad sense, these findings contribute to our understanding of how space and time emerge from an underlying quantum theory. This could potentially be very useful for understanding the earliest part of the Big Bang where space and time emerges.

The researcher has several follow-up plans. Most importantly he is currently studying the Spin Matrix theories that can be used to describe black holes. These Spin Matrix theories have new features that is necessary to understand in detail before one can proceed to study the emerge of a black hole from Spin Matrix theory. Moreover, he plans to study the properties of Spin Matrix theories in more details, such as their correlation functions, together with collaborators. Apart from the interest in black hole, he plans to pursue another general idea, namely that Spin Matrix theory can provide new holographic correspondences that are simpler to study than the previously known correspondences. Therefore, these knew correspondences should enable one to understand quantitatively how space and time emerges from a quantum theory. This research direction is also pursued as part of large project grant from the Independent Research Foundation of Denmark.

The research of the QUNAT project, as well as related projects, are important for getting a better understanding of black holes, but also to understand better the quantum mechanics of gravity. For black holes, we are with the gravitational wave experiments, as well as other astrophysical experiments, closer to be able to make precision measurement of the physics of black holes. This can be used to test Einsteins theory of General Relativity, which is very important. As part of this one tests the physics of the event horizon of black holes. The physics of the event horizon is likely subject to quantum corrections at short distances, and recently several scientist suggested that this give rise to measurable effects.

Apart from experiments it is important for our general understanding of what is in our universe. Black holes are very important for our universe, e.g. there is a gigantic black hole in the middle of our own galaxy for instance. So without an understanding of what a black hole consist of, and what is behind the event horizon, we don’t understand what goes on in our universe.

Finally, the quantum mechanics of gravity, which is related to the microscopic nature of black holes, is important in general, and also specifically for understanding the beginning of our universe.

1) That it was understood how to describe the so-called D-branes using Spin Matrix Theory. D-branes are non-perturbative objects just like black holes, so understand D-branes is a very good step on to understanding black holes. This work was done in Phys. Rev. D 94, no. 6, 066001. It revealed how D-branes, that are described classically in a gravitational background, emergence from a quantum theory, including their interactions. The importance of their interactions is that this allowed for the first time to go beyond the supersymmetric limit of D-branes, since the interactions introduce non-supersymmetric corrections.

2) That a new type of geometry that emerges from Spin Matrix theory has been discovered. This work was done by the researcher with Niels Obers and Jelle Hartong that will be published in Phys. Rev. D. Part of understanding black holes is to understand how geometry emerges from a quantum theory. In this case we are able to understand the emergence of geometry from all Spin Matrix theories. This shows in particular that the emergent geometry is a new type of geometry that has not been considered before.

3) That one can make quantitative description of the thermodynamics of string theory emerging from a holographically dual gauge theory. This work was done by the researcher with Matthias Wilhelm and is expected to be published in Physical Review Letters. This is an important step in describing the thermodynamics of black holes, which are part of string theory, from point of view of a dual quantum theory without gravity. In particular, the thermodynamic phase transition temperature that is described quantitatively in this work is connected to the phase transition to a black hole.

In a broad sense, these findings contribute to our understanding of how space and time emerge from an underlying quantum theory. This could potentially be very useful for understanding the earliest part of the Big Bang where space and time emerges.

The researcher has several follow-up plans. Most importantly he is currently studying the Spin Matrix theories that can be used to describe black holes. These Spin Matrix theories have new features that is necessary to understand in detail before one can proceed to study the emerge of a black hole from Spin Matrix theory. Moreover, he plans to study the properties of Spin Matrix theories in more details, such as their correlation functions, together with collaborators. Apart from the interest in black hole, he plans to pursue another general idea, namely that Spin Matrix theory can provide new holographic correspondences that are simpler to study than the previously known correspondences. Therefore, these knew correspondences should enable one to understand quantitatively how space and time emerges from a quantum theory. This research direction is also pursued as part of large project grant from the Independent Research Foundation of Denmark.

The research of the QUNAT project, as well as related projects, are important for getting a better understanding of black holes, but also to understand better the quantum mechanics of gravity. For black holes, we are with the gravitational wave experiments, as well as other astrophysical experiments, closer to be able to make precision measurement of the physics of black holes. This can be used to test Einsteins theory of General Relativity, which is very important. As part of this one tests the physics of the event horizon of black holes. The physics of the event horizon is likely subject to quantum corrections at short distances, and recently several scientist suggested that this give rise to measurable effects.

Apart from experiments it is important for our general understanding of what is in our universe. Black holes are very important for our universe, e.g. there is a gigantic black hole in the middle of our own galaxy for instance. So without an understanding of what a black hole consist of, and what is behind the event horizon, we don’t understand what goes on in our universe.

Finally, the quantum mechanics of gravity, which is related to the microscopic nature of black holes, is important in general, and also specifically for understanding the beginning of our universe.