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)
