Anomaly-induced edge currents in hydrodynamics with parity anomaly

TL;DR

This paper explores how the parity anomaly in a $(2+1)$-dimensional relativistic hydrodynamics of massless Dirac fermions leads to boundary edge currents, revealing novel transport phenomena linked to topological anomalies.

Contribution

It demonstrates the implementation of the parity anomaly in hydrodynamics, deriving boundary currents and generalizing to multiple anomalies and symmetries.

Findings

Boundary localized $ ext{U}(1)$ and entropy currents identified.

Bulk anomalous current with zero divergence found.

Edge currents have coefficients half of those in $(1+1)$-dimensional chiral transports.

Abstract

In this paper, we discuss relativistic hydrodynamics for a massless Dirac fermion in $(2+1)$ dimensions, which has the parity anomaly -- a global 't Hooft anomaly between $\mathrm{U}(1)$ and parity symmetries. We investigate how hydrodynamics implements the party anomaly, particularly focusing on the transport phenomena at the boundary. Based on the parity anomaly matching and the second law of local thermodynamics, we find $\mathrm{U}(1)$ and entropy currents localized at the boundary as well as the bulk anomalous current with vanishing divergence. These edge currents are similar to the $(1+1)$-dimensional chiral transports, but the coefficients are given by half of theirs. We also generalize our discussion to more general anomalies among multiple $\mathrm{U}(1)$ symmetries and single $\mathbb{Z}_2$ symmetry.