SU(2) slave fermion solution of the Kitaev honeycomb lattice model

We apply the SU(2) slave fermion formalism to the Kitaev honeycomb lattice model. We show that both the toric code phase (the A phase) and the gapless phase of this model (the B phase) can be identified with p-wave superconducting phases of the slave fermions, with nodal lines which, respectively, do not or do intersect the Fermi surface. The non-Abelian Ising anyon phase is a p+ip superconducting phase that occurs when the B phase is subjected to a gap-opening magnetic field. We also discuss the transitions between these phases in this language.