Polar phase of superfluid ${}^3$He: Dirac lines in the parameter and momentum spaces

The time reversal symmetric polar phase of the spin-triplet superfluid ${}^3$He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space $(p_x,p_y,p_z)$, the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters – the components of magnetic field $(H_x,H_y,H_z)$. The bosonic Dirac system lives on the border between the type-I and type-II.