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

This paper was originally designated as a Comment on the paper by R. Jackiw and V. A. Kostelecky, Phys. Rev. Lett. 82, 3572 (1999). It gives an example of a fermionic system in which the CPT-odd Chern-Simons terms in the effective action are unambiguously induced by chiral fermions: superfluid ³He-A. In this system the Lorentz and gauge invariances are both violated at high energy, but the behavior of the system beyond the cutoff is known. This allows one to construct a CPT-odd action which combines the conventional 3+1 CS term and the mixed axial-gravitational CS term discussed by G. E. Volovik and A. Vilenkin, http://xxx.lanl.gov/abs/hep-ph/9905460. The influence of the CS term on the dynamics of the effective gauge field has been observed experimentally in rotating ³He-A. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 3–6 (10 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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