Macroscopic parity violating effects and 3He-A

We discuss parity violating effects in relativistic quantum theory and their analogues in the effective field theory of superfluid 3He−A. A mixed axial-gravitational Chern-Simons term in the relativistic effective action and its condensed matter analogue are responsible for the chiral fermion flux along the rotation axis of the heat bath in a relativistic system and for the unusual Ω-odd dependence of the zero-temperature density of the normal component on the rotation velocity in 3He−A.