Low-energy effective field theory of superfluid 3He-B and its gyromagnetic and Hall responses

TL;DR

This paper develops a comprehensive low-energy effective field theory for superfluid 3He-B, capturing its gyromagnetic and Hall responses in curved space, and revealing a dissipationless Hall viscosity linked to orbital angular momentum.

Contribution

It constructs a symmetry-consistent effective field theory for superfluid 3He-B at zero temperature, including next-to-leading order effects, and demonstrates its ability to reproduce key physical responses.

Findings

Reproduces gyromagnetic responses like magnetization and orbital angular momentum density.

Identifies a dissipationless Hall viscosity with coefficients determined by orbital angular momentum.

Shows elliptical polarization of sound waves due to Hall viscosity.

Abstract

The low-energy physics of a superfluid 3He-B is governed by Nambu-Goldstone bosons resulting from its characteristic symmetry breaking pattern. Here we construct an effective field theory at zero temperature consistent with all available symmetries in curved space, which are the U(1) phase x SU(2) spin x SO(3) orbital gauge invariance and the nonrelativistic general coordinate invariance, up to the next-to-leading order in a derivative expansion. The obtained low-energy effective field theory is capable of reproducing gyromagnetic responses of the superfluid 3He-B, such as a magnetization generated by a rotation and an orbital angular momentum density generated by a magnetic field, in a model-independent and nonperturbative way. We furthermore show that the stress tensor exhibits a dissipationless Hall viscosity with coefficients uniquely fixed by the orbital angular momentum density, which manifests itself as an elliptical polarization of sound wave with an induced transverse component.