On the fermionic signature of the lattice monopoles

We consider fermions in the field of a static Abelian monopole in the Euclidean space time, having in mind applications to the lattice. There exists an infinite number of solutions describing the S-wave fermions and labeled by an imaginary frequency iω. The well known zero mode of Jackiw and Rebbi corresponds to ω = 0. The existence of such modes is a manifestation of instability of the vacuum in the presence of the monopoles and massless fermions. In the Minkowski space the corresponding phenomenon is well known and is a cornerstone of the theory of the magnetic catalysis. We discuss possible implications for the phenomenology.