Gauge theory for topological waves in continuum fluids with odd viscosity

TL;DR

This paper develops a U(1) gauge theory framework for topological waves in 2D fluids with odd viscosity, revealing edge modes and exploring bulk-boundary correspondence in continuum systems.

Contribution

It introduces a Maxwell-Chern-Simons gauge theory for hydrodynamic waves with odd viscosity, linking topological invariants to fluid dynamics.

Findings

Derivation of a gauge theory for topological fluid waves.

Identification of edge modes in the presence of boundaries.

Discussion on the bulk-boundary correspondence in continuum fluids.

Abstract

We consider two-dimensional continuum fluids with odd viscosity under a chiral body force. The chiral body force makes the low-energy excitation spectrum of the fluids gapped, and the odd viscosity allows us to introduce the first Chern number of each energy band in the fluids. Employing a mapping between hydrodynamic variables and U(1) gauge-field strengths, we derive a U(1) gauge theory for topologically nontrivial waves. The resulting U(1) gauge theory is given by the Maxwell-Chern-Simons theory with an additional term associated with odd viscosity. We then solve the equations of motion for the gauge fields concretely in the presence of the boundary and find edge-mode solutions. We finally discuss the fate of bulk-boundary correspondence (BBC) in the context of continuum systems.