  Quantum anomalies give rise to new transport phenomena. In particular a
magnetic field can induce an anomalous current via the chiral magnetic effect
and a vortex in the relativistic fluid can also induce a current via the chiral
vortical effect. The related transport coefficients can be calculated via Kubo
formulas. We evaluate the Kubo formula for the anomalous vortical conductivity
at weak coupling and show that it receives contributions proportional to the
gravitational anomaly coefficient. The gravitational anomaly gives rise to an
anomalous vortical effect even for an uncharged fluid.
