On induced CPT-odd Chern-Simons terms in 3+1 effective action

TL;DR

This paper demonstrates that in superfluid 3He-A, chiral fermions unambiguously induce CPT-odd Chern-Simons terms in the effective action, linking high-energy symmetry violations to observable low-energy phenomena.

Contribution

It provides a concrete example of a physical system where CPT-odd Chern-Simons terms are induced by fermions, clarifying their origin and experimental implications.

Findings

CPT-odd Chern-Simons terms are unambiguously induced in superfluid 3He-A.

The system exhibits Lorentz and gauge invariance violations at high energy.

Experimental effects of Chern-Simons terms are observed in rotating 3He-A.

Abstract

This paper was originally designated as Comment to the paper by R. Jackiw and V. Alan Kostelecky (hep-ph/9901358). We provide an example of the fermionic system, the superfluid 3He-A, in which the CPT-odd Chern-Simons terms in the effective action are unambiguously induced by chiral fermions. In this system the Lorentz and gauge invariances both are violated at high energy, but the behavior of the system beyond the cut-off is known. This allows us to construct the CPT-odd action, which combines the conventional 3+1 Chern-Simons term and the mixed axial-gravitational Chern-Simons term discussed in hep-ph/9905460. The influence of Chern-Simons term on the dynamics of the effective gauge field has been experimentally observed in rotating 3He-A.