Periodic Reporting for period 1 - QEAH (Quantum Entanglement And Holography)
Reporting period: 2015-09-01 to 2017-08-31
The overall objective of this project was to shed light on quantum aspects of gravity through the AdS/CFT correspondence.
To give a flavor of the specific problem addressed, let us discuss black holes.
Black holes were predicted theoretically from Einstein's theory of general relativity in 1916, but still, a century later, continue to inspire awe and trigger our imagination. Why?
For the simple reason that we know very little about them. Scientists are still debating about what would happen if an observer fell into a black hole. It was long suggested that gravity would stretch the observer out until death would occur, some time before he or she reached the centre of the black hole (the singularity). However, recent studies which attempted to incorporate some quantum effects suggested that the black hole horizon would behave like a fire-wall, causing instant death to the observer.
The reason such debates survive a century after the black holes' theoretical prediction, is because we do not yet know how to reconcile Einstein's theory of relativity with quantum physics.
Based on current ideas about string theory, the AdS/CFT correspondence and gravity, we expect that the quantum theory of gravity should be “holographic”. This means that there should exist a description of the physics of gravity in terms of a completely different theory. This alternative description is expected to be given by an ordinary quantum theory -- similar to the one which describes the binding of the constituent quarks and gluons into the nuclei of the atoms – but with one dimension less. It is in this sense that the alternative, holographic description of gravity can be thought of as fundamental, while gravity and spacetime, as emergent notion. This project does not directly address black hole physics, but paves the way to doing so by addressing a simpler issue first: the emergence of a shock-wave geometry from the quantum field theory dynamics.
This is fundamental physics research and is important for society by definition. It caters to the basic need of every human being to understand the surrounding world. Beyond this, it is clear that pushing our boundaries of understanding in this direction will ultimately bring forth new technological advances. This si exactly what happened with a plethora of theoretical physics discoveries.
To give a flavor of the specific problem addressed, let us discuss black holes.
Black holes were predicted theoretically from Einstein's theory of general relativity in 1916, but still, a century later, continue to inspire awe and trigger our imagination. Why?
For the simple reason that we know very little about them. Scientists are still debating about what would happen if an observer fell into a black hole. It was long suggested that gravity would stretch the observer out until death would occur, some time before he or she reached the centre of the black hole (the singularity). However, recent studies which attempted to incorporate some quantum effects suggested that the black hole horizon would behave like a fire-wall, causing instant death to the observer.
The reason such debates survive a century after the black holes' theoretical prediction, is because we do not yet know how to reconcile Einstein's theory of relativity with quantum physics.
Based on current ideas about string theory, the AdS/CFT correspondence and gravity, we expect that the quantum theory of gravity should be “holographic”. This means that there should exist a description of the physics of gravity in terms of a completely different theory. This alternative description is expected to be given by an ordinary quantum theory -- similar to the one which describes the binding of the constituent quarks and gluons into the nuclei of the atoms – but with one dimension less. It is in this sense that the alternative, holographic description of gravity can be thought of as fundamental, while gravity and spacetime, as emergent notion. This project does not directly address black hole physics, but paves the way to doing so by addressing a simpler issue first: the emergence of a shock-wave geometry from the quantum field theory dynamics.
This is fundamental physics research and is important for society by definition. It caters to the basic need of every human being to understand the surrounding world. Beyond this, it is clear that pushing our boundaries of understanding in this direction will ultimately bring forth new technological advances. This si exactly what happened with a plethora of theoretical physics discoveries.
In this project we made an important step towards the objective advocated above, first by detailing the emergence of the a shock wave geometry from the field theory dynamics, and then by revealing how to express standard gravitational quantities in terms of their underlying microscopic, holographic description.
Our strategy was to consider a certain field theoretic object, a four-point correlation function, which is expected to correspond to a two-to-two scattering of gravitating particles. Our goal was to make this manifest.
Computing this correlation function is technically involved. We were able to simplify the calculation by focusing on a special limit. In the gravity language this limit corresponds to the scattering of very fast-moving particles.
Once we had the result, we had to check whether it satisfies a certain consistency condition, called unitarity. Quantum systems must satisfy the property of unitarity, otherwise probabilities calculated in physical processes will not always lie between zero and one.
What did we show ?
Einstein's theory of gravity predicts that to some approximation, when two very fast particles collide with each other, they continue their way almost undisturbed except for one effect: they experience a time-delay. Our work described how to obtain the exact same expression for the time-delay, in terms of a completely different quantity naturally defined in the alternative holographic description of gravity. This quantity is a specific Fourier transform of a four-point correlation function.
Fast traveling particles have an interesting effect on the space surrounding them; they produce curvature (shock-wave geometry). Our work explained how to obtain the description of the spacetime formed around a fast traveling object using quantities naturally defined in the holographic description of gravity. In particular, the metric function of the shock-wave geometry was identified with the stress-tensor conformal block in a special limit (the Regge limit).
But more importantly, we were able to explicitly show that a certain class of ordinary quantum field theories, conformal field theories, have an equivalent description in terms of a specific theory of gravity: Einstein's gravity theory. For instance, we showed that under certain assumptions, the theory contains particles of maximum spin equal to two, with properties matching those of the graviton. We also showed that other theories of gravity, e.g. Lanczos-Gauss-Bonnet gravity, cannot arise from a consistent CFT.
Outline of Results (3 publications and one in print):
I. Cortese and M. Kulaxizi, “General backgrounds for higher spin massive particles,” arXiv:1711.xxxxx
F.J. Garcia Abda, M. Kulaxizi and A. Parnachev, “On Complexity of Holographic Flavors,” arXiv:1705.08424
M. Kulaxizi, A. Parnachev and A. Zhiboedov, “Bulk Phase Shift, CFT Regge Limit and Einstein Gravity,” arXiv:1705.02934
Z. Komargodski, M. Kulaxizi, A. Parnachev and A. Zhiboedov, “Conformal Field Theories and Deep Inelastic Scattering,” Phys. Rev. D 95, 065011 (2017) [arXiv:1601.05453 [hep-th]].
Presentation of the project's results at seminars and workshops/conferences:
• “Einstein Gravity from CFT Regge Physics,”
— INFN, Theory Group, University of Naples, Naples (Nov, 2017)
— Holography and Quantum Matter Workshop, IFT, Madrid (Sep, 2017)
— Gravity: New perspectives from Strings and Higher Dimensions, Benasque, (July, 2017)
— 9th Regional Meeting in String Theory, Kolymbari, Crete (July, 2017)
• “Constraints in unitary CFTs with gravitational duals,”
— 48th Meeting of the the North British Mathematical Physics Seminar, Durham, (Nov, 2016)
— Edinburgh Theoretical Seminar Series, Heriot-Watt, Edinburgh, (Nov, 2016)
• “CFTs and constraints on their three-point functions,”
— Black Holes and Emergent Spacetime, Nordita-Stockholm, (Sep, 2016)
— Irish Quantum Foundations Meeting (IQF), Maynooth University, Dublin (May, 2016)
— Theory Group, University of Milano-Bicocca, Milan, (May, 2016)
— DESY Hamburg Theory Group, Hamburg, (April 2016)
— Theoretical Physics Group, Queen Mary University of London, (April, 2016)
Our strategy was to consider a certain field theoretic object, a four-point correlation function, which is expected to correspond to a two-to-two scattering of gravitating particles. Our goal was to make this manifest.
Computing this correlation function is technically involved. We were able to simplify the calculation by focusing on a special limit. In the gravity language this limit corresponds to the scattering of very fast-moving particles.
Once we had the result, we had to check whether it satisfies a certain consistency condition, called unitarity. Quantum systems must satisfy the property of unitarity, otherwise probabilities calculated in physical processes will not always lie between zero and one.
What did we show ?
Einstein's theory of gravity predicts that to some approximation, when two very fast particles collide with each other, they continue their way almost undisturbed except for one effect: they experience a time-delay. Our work described how to obtain the exact same expression for the time-delay, in terms of a completely different quantity naturally defined in the alternative holographic description of gravity. This quantity is a specific Fourier transform of a four-point correlation function.
Fast traveling particles have an interesting effect on the space surrounding them; they produce curvature (shock-wave geometry). Our work explained how to obtain the description of the spacetime formed around a fast traveling object using quantities naturally defined in the holographic description of gravity. In particular, the metric function of the shock-wave geometry was identified with the stress-tensor conformal block in a special limit (the Regge limit).
But more importantly, we were able to explicitly show that a certain class of ordinary quantum field theories, conformal field theories, have an equivalent description in terms of a specific theory of gravity: Einstein's gravity theory. For instance, we showed that under certain assumptions, the theory contains particles of maximum spin equal to two, with properties matching those of the graviton. We also showed that other theories of gravity, e.g. Lanczos-Gauss-Bonnet gravity, cannot arise from a consistent CFT.
Outline of Results (3 publications and one in print):
I. Cortese and M. Kulaxizi, “General backgrounds for higher spin massive particles,” arXiv:1711.xxxxx
F.J. Garcia Abda, M. Kulaxizi and A. Parnachev, “On Complexity of Holographic Flavors,” arXiv:1705.08424
M. Kulaxizi, A. Parnachev and A. Zhiboedov, “Bulk Phase Shift, CFT Regge Limit and Einstein Gravity,” arXiv:1705.02934
Z. Komargodski, M. Kulaxizi, A. Parnachev and A. Zhiboedov, “Conformal Field Theories and Deep Inelastic Scattering,” Phys. Rev. D 95, 065011 (2017) [arXiv:1601.05453 [hep-th]].
Presentation of the project's results at seminars and workshops/conferences:
• “Einstein Gravity from CFT Regge Physics,”
— INFN, Theory Group, University of Naples, Naples (Nov, 2017)
— Holography and Quantum Matter Workshop, IFT, Madrid (Sep, 2017)
— Gravity: New perspectives from Strings and Higher Dimensions, Benasque, (July, 2017)
— 9th Regional Meeting in String Theory, Kolymbari, Crete (July, 2017)
• “Constraints in unitary CFTs with gravitational duals,”
— 48th Meeting of the the North British Mathematical Physics Seminar, Durham, (Nov, 2016)
— Edinburgh Theoretical Seminar Series, Heriot-Watt, Edinburgh, (Nov, 2016)
• “CFTs and constraints on their three-point functions,”
— Black Holes and Emergent Spacetime, Nordita-Stockholm, (Sep, 2016)
— Irish Quantum Foundations Meeting (IQF), Maynooth University, Dublin (May, 2016)
— Theory Group, University of Milano-Bicocca, Milan, (May, 2016)
— DESY Hamburg Theory Group, Hamburg, (April 2016)
— Theoretical Physics Group, Queen Mary University of London, (April, 2016)
The results outlined above, go beyond the state-of-the-art in the field and answer some critical questions which are central in order to promote our understanding of quantum gravity.
In particular, our results provide the indispensable step in the effort to understand how the black hole geometry emerges from a purely holographic/field theoretic description. This is exactly the current focus of my work together with my collaborators.
This project has thus far impacted directly the youth of the society by exciting their curiosity about the physical world and directing them to further study theoretical physics.This is an observation made during my appointment at the School of Mathematics, Trinity College Dublin for the last years. I expect that a larger and more obvious societal impact will follow the publication of the answers to the fundamental questions about black holes we are able to research as a result of this project.
In particular, our results provide the indispensable step in the effort to understand how the black hole geometry emerges from a purely holographic/field theoretic description. This is exactly the current focus of my work together with my collaborators.
This project has thus far impacted directly the youth of the society by exciting their curiosity about the physical world and directing them to further study theoretical physics.This is an observation made during my appointment at the School of Mathematics, Trinity College Dublin for the last years. I expect that a larger and more obvious societal impact will follow the publication of the answers to the fundamental questions about black holes we are able to research as a result of this project.