Orbital momentum of chiral superfluids and spectral asymmetry of edge states

This is comment to preprint arXiv:1409.7459 by Y. Tada, Wenxing Nie and M. Oshikawa “Orbital angular momentum and spectral flow in two dimensional chiral superfluids”, where the effect of spectral flow along the edge states on the magnitude of the orbital angular momentum is discussed. The general conclusion of the preprint on the essential reduction of the angular momentum for the higher values of chirality, $|\nu|>1$, is confirmed. However, we show that if parity is violated, the reduction of the angular momentum takes place also for the $p$-wave superfluids with $|\nu|=1$.