Topology of chiral superfluid: skyrmions, Weyl fermions and chiral anomaly

Chiral anomaly observed in the chiral superfluid $^3$He-A is the result of the combined effect of the real space and momentum space topologies. This effect incorporates several topological charges in the extended $(\mathbf{k, r})$-space, which is beyond the conventional chiral anomaly in the relativistic systems.