Relativistic hydrodynamics with the parity anomaly

TL;DR

This paper investigates how the parity anomaly influences hydrodynamic behavior in 2+1D quantum field theories, revealing new constraints on non-dissipative transport coefficients through anomaly inflow and thermodynamic principles.

Contribution

It demonstrates that the parity anomaly and bulk SPT phase considerations impose novel restrictions on non-dissipative transport coefficients in 2+1D hydrodynamics.

Findings

Quantized Hall conductivity fixed at σ_xy = e^2/2h.

Derived new constraints on three non-dissipative parity-odd transport coefficients.

Extended understanding of anomaly effects in hydrodynamic regimes.

Abstract

We consider the hydrodynamic regime of a 2+1 dimensions QFT with the parity anomaly. Beyond the known constraints from positivity of entropy production, we show that the anomaly inflow mechanism, from a corresponding bulk SPT phase, together with thermodynamic consistency of equilibrium partition functions, restricts the form of non-dissipative transport coefficients. This included the known form of quantised Hall conductivity, which is fixed to be $\sigma_{xy} = e^2/2h$, along with new constraints on other three non-dissipative parity-odd transport coefficients.