Topological fluids in condensed matter systems

The phenomenological Chern-Simons-Ginzburg-Landau (CSGL) model for fractional quantum Hall states gives rise to hydrodynamic-like equations of motion with a density-vorticity constraint. This constraint stems from the topological Chern-Simons term and encodes the macroscopic "quantum" effects. In this talk, we will discuss a reformulation of CSGL action in terms of a classical fluid Lagrangian with a topological term. Such a fluid action with a topological term was recently written to describe a fluid with a dense collection of vortices by Nair in arXiv:2008.11260. We discuss a systematic derivation of the topological fluid action starting from CSGL theory. We show that the role of the topological term in the fluid language is completely different from the Chern-Simons term of the CSGL action and the density vorticity constraint must be imposed using a Lagrange multiplier. In fact this connection is more general and allows us to express any charged bosonic condensate in terms of classical fluids with topological terms. Expressing condensed matter systems in terms of a fluid action with a topological term enables us to import the framework of linear and non-linear fluid dynamical phenomena within the ambit of topological orders studied in condensed matter systems.