Abelian Chern-Simons Term in Superfluid 3He-A

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.

16 pages, 2 figures, LaTeX, minor points are changed, references are added. Accepted for publication in Physics Letters A

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