Anomalies, Geometry, and Hydrodynamics

My research program is devoted to studies of emergent properties in systems without parity symmetry. Ultimately it is meant to understand the interplay between symmetry and topology in effective field theories and their connections to fluid mechanics and kinetic theory.

Modern understanding of physics is based on the description in terms of effective field theories. In order to understand phenomena at a given scale we do not need to know the theory of everything but we need to develop an effective description, suitable for scales we want to understand. Perhaps the oldest example of an effective field theory is hydrodynamics, a theory that parameterizes our ignorance of high-energy, microscopic degrees of freedom by reducing it to a set of parameters, called transport coefficients. They are supplemented with dynamical fields such as fluid velocity. Another effective description of many-body physics, at a different level of “coarse-graining”, is kinetic theory. It allows one to understand wider range of scales and give a more microscopic analysis. The effective model relevant at macroscopic scales is often classical and does not employ quantization. However, it does not always mean that a correct macroscopic theory has to be ignorant about the details of the quantum world. In fact quantum phenomena can exhibit surprising ramifications at macroscopic scales. The oldest example includes super-fluidity and a more recent illustration of such phenomena includes quantum Hall fluids in two spatial dimensions and fluids with axial quantum anomalies in three spatial dimensions. Both quantum Hall fluids and anomalous fluids are examples of parity-breaking hydrodynamics. In consequence a proper formulation of macroscopic physics in systems that break parity is of great relevance. Parity breaking may be crucial to a wide range of phenomena from the early Universe, to heavy-ion collisions, neutron stars, relativistic astrophysical systems, and new materials such as graphene. The number of experimental examples that allows one to analyze parity-odd fluids is growing, due to novel, exotic materials.