Lifshitz Transition in the Double-Core Vortex in ^{3}He-B.

We study the spectrum of fermion states localized within the vortex core of a weak-coupling p-wave superfluid. The low energy spectrum consists of two anomalous branches that generate a large density of states at the locations of the half cores of the vortex. Fermi liquid interactions significantly stretch the vortex structure, which leads to a Lifshitz transition in the effective Fermi surface of the vortex core fermions. We apply the results to the rotational dynamics of vortices in superfluid ^{3}He-B and find an explanation for the observed slow mode.