On chiral vortical effect in accelerated matter

We revisit the evaluation of the chiral vortical effect in the accelerated matter. To first order in the acceleration the corresponding matrix element of the axial current can be reconstructed from the flat-space limit. A crucial point is the existence in the this case of an extra conservation law of fluid helicity. As a result, the chirality of the microscopic degrees of freedom and helicity of the macroscopic motion are separately conserved. This separation persists also in presence of gravity. Implications for the thermal chiral vortical effect are discussed.