## Final Report Summary - STRINGS MEET REALITY (Applications of the AdS/CFT correspondence to particle physics and condensed matter systems)

This research project employed and expanded the state-of-the-art methods based on field theory, hydrodynamics, and topology to understand the physics of strongly-coupled field theories. The motivation for such an endeavor came from two directions: high-energy experiments with heavy-ion collisions and condensed matter experiments with Weyl fermions and cold atoms.

Heavy-ion collisions are supposed to improve our understanding of the phase of matter present instantly after the Big Bang. The state of matter consist of elementary particles called quarks and gluons, which interact through the so-called strong interactions. In technical terms, gluons are vector gauge bosons that mediate strong interactions of quarks. Gluons themselves carry the color charge of the strong interaction. The theoretical description of strongly interacting quarks and gluons is known as Quantum Chromodynamics (QCD). At low temperatures QCD describes hadronic degrees of freedom e.g. protons and neutrons, which are the building blocks of atomic nuclei. At high-temperatures quarks and gluons are deconfined into a gas of quarks and gluons – a quark-gluon plasma (QGP). Recent advances in heavy-ion experiments in Relativistic Heavy Ion Collider and Large Hadron Collider allow us to create QGP and study its properties. The fundamental lesson of those experiments is that QGP behaves a strongly coupled liquid, whose evolution is described by the equations of fluid dynamics. The modern formulation of hydrodynamics is captured by the so-called effective field theory, i.e. theory that parameterizes our ignorance of high-energy, microscopic degrees of freedom by reducing it to a set of parameters, called transport coefficients (e.g. viscosity), supplemented with dynamical fields such as fluid velocity. Quark-gluon plasma is a quantum fluid, therefore it can have richer properties than its classical counterpart. One example which shows that quantum fluids have distinct properties It connects quantum field theory (QFT) anomalies and the hydrodynamic regime. In quantum physics anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of the full quantum theory. Another example is the dynamics of a colored fluid charged under non-Abelian Yang-Mills gauge fields, where the constituents of the fluid carry non-Abelian color charges and interact with non-Abelian fields. Due to its non-Abelian nature, we this system gives rise to a variety of physical phenomena richer than its Abelian counterpart, viz. electromagnetic plasma. The detailed understanding of these features is still incomplete.

The second line of research which motivated this project came from condensed matter experiments with Weyl fermions. An important feature of Weyl fermions is that they break parity through the quantum anomaly phenomenon. While it was known for a long time that anomalies induce observable effects in quantum field theories, only quite recently it has become clear that anomalies also have important macroscopic manifestations and affect transport and hydrodynamics. The effects of anomalies are especially important in the systems that possess chiral fermions (e.g. quantum Hall systems, graphene or quark-gluon plasma) and where topologically non-trivial configurations such as vortices are present. The proper mathematical language to describe anomalies requires topology. It is concerned with the properties of space that are preserved under smooth deformations, such as stretching or bending, but not tearing and gluing. The first topological state that was observed is the ‘quantum Hall effect’ — an induced voltage in a current-carrying conductor exposed to a magnetic field. The conductor is confined to two dimensions. When current flows longitudinally through the conductor, a transverse voltage is measured. As the magnetic field increases gradually, the ratio of current to voltage, called the Hall conductance, increases by discrete jumps. The values are integer multiples of a fundamental conductance unit. We now understand that the Hall conductance is a topological invariant. The drawback of QHE is that it requires a very high magnetic field, which makes it unsuitable for technological applications.

It was long believed that the magnetic field is necessary. Without it, the topological properties and the quantized conductance are destroyed. It was recently realized that topological states can exist without magnetic fields thanks to the spin-orbit coupling. The most prominent example of such material are topological insulators — materials that only conduct electricity on their surfaces. One type of such materials is the so-called Weyl semimetals, characterized by the the presence of points of electronic band touching. The properties of fermionic topological phases are currently intensively studied and hydrodynamic properties are an important part of that. Topological insulators are considered the future of electronics. They are electrical insulators in the bulk and have surface states that conduct electrons extremely well. The topology protects the surface currents from disorder and impurities. By further combining topological insulators with a superconductor, which conducts electricity with no resistance, it may be possible to build a quantum computer. Such a technology would perform calculations using the laws of quantum mechanics, making them much faster than conventional computers at certain tasks such..

This project shed light on various aspects of quantum hydrodynamics. The work done during its course elucidated both phenomenological and formal aspects of hydrodynamics of quantum fluids. It was theoretical but it provides a basis for further developments in experiments, which are expected to be crucial for future electronics and quantum computing. In this respect, the results obtained significantly enhance our scientific knowledge and have a potential for transforming society through new computing developments.

Heavy-ion collisions are supposed to improve our understanding of the phase of matter present instantly after the Big Bang. The state of matter consist of elementary particles called quarks and gluons, which interact through the so-called strong interactions. In technical terms, gluons are vector gauge bosons that mediate strong interactions of quarks. Gluons themselves carry the color charge of the strong interaction. The theoretical description of strongly interacting quarks and gluons is known as Quantum Chromodynamics (QCD). At low temperatures QCD describes hadronic degrees of freedom e.g. protons and neutrons, which are the building blocks of atomic nuclei. At high-temperatures quarks and gluons are deconfined into a gas of quarks and gluons – a quark-gluon plasma (QGP). Recent advances in heavy-ion experiments in Relativistic Heavy Ion Collider and Large Hadron Collider allow us to create QGP and study its properties. The fundamental lesson of those experiments is that QGP behaves a strongly coupled liquid, whose evolution is described by the equations of fluid dynamics. The modern formulation of hydrodynamics is captured by the so-called effective field theory, i.e. theory that parameterizes our ignorance of high-energy, microscopic degrees of freedom by reducing it to a set of parameters, called transport coefficients (e.g. viscosity), supplemented with dynamical fields such as fluid velocity. Quark-gluon plasma is a quantum fluid, therefore it can have richer properties than its classical counterpart. One example which shows that quantum fluids have distinct properties It connects quantum field theory (QFT) anomalies and the hydrodynamic regime. In quantum physics anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of the full quantum theory. Another example is the dynamics of a colored fluid charged under non-Abelian Yang-Mills gauge fields, where the constituents of the fluid carry non-Abelian color charges and interact with non-Abelian fields. Due to its non-Abelian nature, we this system gives rise to a variety of physical phenomena richer than its Abelian counterpart, viz. electromagnetic plasma. The detailed understanding of these features is still incomplete.

The second line of research which motivated this project came from condensed matter experiments with Weyl fermions. An important feature of Weyl fermions is that they break parity through the quantum anomaly phenomenon. While it was known for a long time that anomalies induce observable effects in quantum field theories, only quite recently it has become clear that anomalies also have important macroscopic manifestations and affect transport and hydrodynamics. The effects of anomalies are especially important in the systems that possess chiral fermions (e.g. quantum Hall systems, graphene or quark-gluon plasma) and where topologically non-trivial configurations such as vortices are present. The proper mathematical language to describe anomalies requires topology. It is concerned with the properties of space that are preserved under smooth deformations, such as stretching or bending, but not tearing and gluing. The first topological state that was observed is the ‘quantum Hall effect’ — an induced voltage in a current-carrying conductor exposed to a magnetic field. The conductor is confined to two dimensions. When current flows longitudinally through the conductor, a transverse voltage is measured. As the magnetic field increases gradually, the ratio of current to voltage, called the Hall conductance, increases by discrete jumps. The values are integer multiples of a fundamental conductance unit. We now understand that the Hall conductance is a topological invariant. The drawback of QHE is that it requires a very high magnetic field, which makes it unsuitable for technological applications.

It was long believed that the magnetic field is necessary. Without it, the topological properties and the quantized conductance are destroyed. It was recently realized that topological states can exist without magnetic fields thanks to the spin-orbit coupling. The most prominent example of such material are topological insulators — materials that only conduct electricity on their surfaces. One type of such materials is the so-called Weyl semimetals, characterized by the the presence of points of electronic band touching. The properties of fermionic topological phases are currently intensively studied and hydrodynamic properties are an important part of that. Topological insulators are considered the future of electronics. They are electrical insulators in the bulk and have surface states that conduct electrons extremely well. The topology protects the surface currents from disorder and impurities. By further combining topological insulators with a superconductor, which conducts electricity with no resistance, it may be possible to build a quantum computer. Such a technology would perform calculations using the laws of quantum mechanics, making them much faster than conventional computers at certain tasks such..

This project shed light on various aspects of quantum hydrodynamics. The work done during its course elucidated both phenomenological and formal aspects of hydrodynamics of quantum fluids. It was theoretical but it provides a basis for further developments in experiments, which are expected to be crucial for future electronics and quantum computing. In this respect, the results obtained significantly enhance our scientific knowledge and have a potential for transforming society through new computing developments.