Abelian Chern-Simons term in superfluid 3He-A

Abstract

We show in this paper that an Abelian Chern-Simons term is induced in (2 + 1)- and (3 + 1)-dimensional rotating superfluid 3He-A and that it plays an important role in its dynamics. Because U(1) symmetry is spontaneously broken in 3He-A, a Goldstone mode appears and contributes to the induced Chern-Simons term. We found that the coefficient of the 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 3He-A in a cylinder geometry is derived from the Chern-Simons term.