Abelian Chern-Simons Term in Superfluid 3He-A

TL;DR

This paper demonstrates that an Abelian Chern-Simons term is induced in rotating superfluid helium-3 A-phase, affecting its dynamics and linking to observable quantities like Hall conductance and orbital angular momentum.

Contribution

It reveals the induction of the Chern-Simons term in superfluid helium-3 A-phase and its dependence on Goldstone modes and infrared cutoffs, providing new insights into its topological properties.

Findings

Chern-Simons term is induced in 2+1 and 3+1 dimensions.

The coefficient depends on the infrared cutoff of Goldstone modes.

Orbital angular momentum is derived from the Chern-Simons term.

Abstract

We show in this paper that Abelian Chern-Simons term is induced in 2+1 and 3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A, Goldstone mode appears and contributes to induced Chern-Simons term. We found that the coefficient of Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut off of the Goldstone mode, and that the orbital angular momentum of $^{3}$He-A in a cylinder geometry is derived from Chern-Simons term.