Quantum Anomalies, Topology, and Hydrodynamics

Quantum Anomalies, Topology, and Hydrodynamics

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Organized by Alexander Abanov, Dmitri Kharzeev, Boris Khesin, Dam Son, and Paul Wiegmann
February 17-June 13, 2014

Recent developments in relativistic hydrodynamics place it at the crossroads of nuclear physics, condensed matter physics and string theory. Hydrodynamics is known to be very effective in describing the long-wavelength behavior of many body systems regardless of the strength of inter-particle interactions. It encapsulates general conservation laws and symmetries of the system.

Quantum anomalies can break some of the symmetries of the underlying theory. 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 — in particular, anomalies make possible non-dissipative transport and bring to the existence novel collective excitations. 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 are present (e.g. vortices, skyrmions or sphalerons).

An important advantage of hydrodynamics is that it is formulated explicitly in terms of physical observables. Therefore, the hydrodynamical approach usually leads directly to the predictions for the experiment, both in condensed matter and nuclear physics. Furthermore, topological methods in hydrodynamics could shed some light on the search for new symmetries related to quantum anomalies. Topological fluid dynamics is a young branch of mathematics which studies group symmetries of various equations of hydrodynamical origin, as well as geometric and topological properties of their solutions and of the corresponding magnetic and vortex fields. The interaction of the relativistic and topological approaches in hydrodynamics might also lead to new insights into the turbulence and singularity problems.

The goal of the program is to develop hydrodynamic descriptions in condensed matter physics and QCD at finite temperature and density with an emphasis on the effects of quantum anomalies and topology. Among these effects is the non-dissipative transport of charges and energy — with a wide range of applications in science and technology, from quantum computing to the detection of topological fluctuations of QCD in heavy ion collisions. We aim at advancing quantum hydrodynamics through the use of topological and geometric methods.