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

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.