Anomalous chiral Fermi surfaces

We provide a geometrical argument for the emergence of a Wess-Zumino-Witten (WZW) term in a Fermi surface threaded by a Berry curvature. In the presence of external fields, the gauged WZW term yields a chiral (triangle) anomaly for the fermionic current at the edge of the Fermi surface. The fermion number is conserved, though, since Berry curvatures always occur in pairs with opposite (monopole) charge. The anomalous vector and axial currents for a fermionic fluid at low temperature threaded by pairs of Berry curvatures are discussed. The leading temperature correction to the chiral vortical effect in a slowly rotating Fermi surface threaded by a Berry curvature may be tied to the gravitational anomaly.