## Final Report Summary - GAUGEGRAVITYMUNICH (Non Perturbative Physics at Finite Temperature: Field Theory and Holography)

One of the most fruitful fields in modern physics is the study of nuclear matter under extreme conditions, which means very high temperatures and/or densities. Theories at high temperature, and low density, are relevant for the collisions of large nuclei at ultra-relativistic energies. The nature of the Quark-Gluon Plasma, which is produced in such conditions, impacts directly unto our understanding of experiments with heavy ions, underway at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, and most recently also at the Large Hadron Collider (LHC) at CERN. Quantum anomalies are one of the most subtle effects in relativistic field theory, and they are responsible for some transport phenomena in the Quark-Gluon Plasma: one of them is the chiral magnetic effect, characterized by the generation of an electric current induced by a magnetic field in the plasma, and another one related to it is the chiral vortical effect, in which the electric current is induced by a vortex. While the experimental measurement of anomalous transport properties are very difficult in heavy ion physics, there are special materials that are an excellent laboratory check of these effects. In particular, these anomalies can be realized also in condensed matter systems, like Weyl semi-metals, and this would allow testing these transport phenomena experimentally in a controlled environment. On the other hand, the initial stages of the Quark-Gluon Plasma thermalization is affected by far from equilibrium dynamics which nowadays is not well understood. It is crucial to have a reliable picture of the time evolution of the heat flow and the entropy production of heavy ions to understand the dynamics of the plasma.

The principal purpose of this project has been a comprehensive study, from a theoretic perspective, of the properties of fundamental interactions at finite temperature and chemical potential, focused on the modern theory of strong interactions - Quantum Chromodynamics, beyond the Standard Model Physics, and Condensed Matter Systems. The project is summarized in four main research lines:

1. Hydrodynamics of Relativistic Fluids and Anomalies.

2. Physics of heavy quarks and Polyakov loop.

3. Study of a holographic approach for Weyl semi-metals.

4. Holographic realization of the Higgs boson: study of properties of a naturally light dilaton.

The research includes the study of hydrodynamic properties of relativistic fluids and their implications for the Quark-Gluon Plasma as well as anomalous processes in condensed matter systems. It has been studied as well the far-from-equilibrium dynamics of strongly correlated systems. The study of these topics has been carried out by using a wide variety of techniques based on the Anti-de Sitter/CFT correspondence and Thermal Field Theory. We have put special emphasis on the AdS/CFT, as historically this formalism has given some important insight about the universal properties of the dynamics of the systems. An example is the universal bound on the ratio of shear viscosity to entropy density, already obtained one decade ago.

We have found important results in all these topics. In particular, within the study of far-from-equilibrium dynamics in AdS/CFT, we obtained a universal time-evolution behavior of the system. This will lead to a profound impact of our understanding of the quenched properties of these kind of systems, and will have important implications for the physics of the Quark-Gluon Plasma dynamics in the future.

While it is difficult to measure anomalous transport effects in the Quark-Gluon plasma, there are some materials that can be easily realizable in the laboratory and that present these transport properties as well. We have studied the chiral magnetic and chiral vortical effects in Weyl semi-metals within the AdS/CFT formalism. These properties have been studied as well in other condensed matter systems affected by disorder, and found that contrary to the electric conductivity, the anomalous effects are insensitive to disorder. In addition, we have found a regime in which the electric conductivity vanishes, so that the systems behave as insulators. An important consequence of this is that one can study the anomalous properties of these systems in a clean way.

On the heavy quark physics we were able to describe the thermodynamics of a pair of heavy quark-antiquark in the confined phase of QCD, based on a representation of this observable in terms of hadrons, which are the bound states of QCD in this regime. Important results were obtained, not only for the free energy, but also for other observables like the entropy and specific heat, all of them predictions that deserve to be confirmed in the future with lattice simulations. One important ingredient in this description is the existence of an avoided crossing pattern between the string tension connecting the two heavy quarks, and the hadron states. Our prediction confirms and extend previous studies on the avoided crossing, by using a totally different approach based on the thermodynamics of the system.

By using AdS/CFT techniques applied to particle physics, we have studied in details the physics of the new resonances recently reported in the LHC, in particular the Higgs boson reported in 2012, and the diphoton excess reported in Dec 2015. In addition, some deviations from the Standard Model predictions have been studied in details, in particular the LHCb flavour anomalies related to the decay of B mesons into muons, and the long-standing problem of the anomalous magnetic moment of the muon. We have used a scenario based on an extension of the Standard Model with extra-dimensions, which predicts the existence of new particles, most of them quite heavy and so difficult to be measured – this is the case of the Kaluza-Klein modes of the Z boson and photon. However, a particular realization of this scenario leads to the existence of a light particle called the dilaton. In this work we have studied both kind of particles, and we were able to describe the diphoton excess as due to a light dilaton in the spectrum, and the LHCb flavour anomalies as effects produced by the Kaluza-Klein modes.

The results of the project have been published up to the present in 5 peer-reviewed publications, and 15 publications in Conference Proceedings, and some other peer-reviewed publications are expected after the end of the project. In addition, these results have been presented in 17 international conferences, and in 6 invited seminars in Universities and International Research Institutions of the European Union and America. The results obtained in this project will have important implications in the future for the physics of heavy ions at RHIC and LHC, Condensed Matter physics and Cosmology.

The principal purpose of this project has been a comprehensive study, from a theoretic perspective, of the properties of fundamental interactions at finite temperature and chemical potential, focused on the modern theory of strong interactions - Quantum Chromodynamics, beyond the Standard Model Physics, and Condensed Matter Systems. The project is summarized in four main research lines:

1. Hydrodynamics of Relativistic Fluids and Anomalies.

2. Physics of heavy quarks and Polyakov loop.

3. Study of a holographic approach for Weyl semi-metals.

4. Holographic realization of the Higgs boson: study of properties of a naturally light dilaton.

The research includes the study of hydrodynamic properties of relativistic fluids and their implications for the Quark-Gluon Plasma as well as anomalous processes in condensed matter systems. It has been studied as well the far-from-equilibrium dynamics of strongly correlated systems. The study of these topics has been carried out by using a wide variety of techniques based on the Anti-de Sitter/CFT correspondence and Thermal Field Theory. We have put special emphasis on the AdS/CFT, as historically this formalism has given some important insight about the universal properties of the dynamics of the systems. An example is the universal bound on the ratio of shear viscosity to entropy density, already obtained one decade ago.

We have found important results in all these topics. In particular, within the study of far-from-equilibrium dynamics in AdS/CFT, we obtained a universal time-evolution behavior of the system. This will lead to a profound impact of our understanding of the quenched properties of these kind of systems, and will have important implications for the physics of the Quark-Gluon Plasma dynamics in the future.

While it is difficult to measure anomalous transport effects in the Quark-Gluon plasma, there are some materials that can be easily realizable in the laboratory and that present these transport properties as well. We have studied the chiral magnetic and chiral vortical effects in Weyl semi-metals within the AdS/CFT formalism. These properties have been studied as well in other condensed matter systems affected by disorder, and found that contrary to the electric conductivity, the anomalous effects are insensitive to disorder. In addition, we have found a regime in which the electric conductivity vanishes, so that the systems behave as insulators. An important consequence of this is that one can study the anomalous properties of these systems in a clean way.

On the heavy quark physics we were able to describe the thermodynamics of a pair of heavy quark-antiquark in the confined phase of QCD, based on a representation of this observable in terms of hadrons, which are the bound states of QCD in this regime. Important results were obtained, not only for the free energy, but also for other observables like the entropy and specific heat, all of them predictions that deserve to be confirmed in the future with lattice simulations. One important ingredient in this description is the existence of an avoided crossing pattern between the string tension connecting the two heavy quarks, and the hadron states. Our prediction confirms and extend previous studies on the avoided crossing, by using a totally different approach based on the thermodynamics of the system.

By using AdS/CFT techniques applied to particle physics, we have studied in details the physics of the new resonances recently reported in the LHC, in particular the Higgs boson reported in 2012, and the diphoton excess reported in Dec 2015. In addition, some deviations from the Standard Model predictions have been studied in details, in particular the LHCb flavour anomalies related to the decay of B mesons into muons, and the long-standing problem of the anomalous magnetic moment of the muon. We have used a scenario based on an extension of the Standard Model with extra-dimensions, which predicts the existence of new particles, most of them quite heavy and so difficult to be measured – this is the case of the Kaluza-Klein modes of the Z boson and photon. However, a particular realization of this scenario leads to the existence of a light particle called the dilaton. In this work we have studied both kind of particles, and we were able to describe the diphoton excess as due to a light dilaton in the spectrum, and the LHCb flavour anomalies as effects produced by the Kaluza-Klein modes.

The results of the project have been published up to the present in 5 peer-reviewed publications, and 15 publications in Conference Proceedings, and some other peer-reviewed publications are expected after the end of the project. In addition, these results have been presented in 17 international conferences, and in 6 invited seminars in Universities and International Research Institutions of the European Union and America. The results obtained in this project will have important implications in the future for the physics of heavy ions at RHIC and LHC, Condensed Matter physics and Cosmology.