Generalized unparticles, zeros of the Green function, and momentum space topology of the lattice model with overlap fermions

摘要

The definition of topological invariants $\tilde{\cal N}_4, \tilde{\cal N}_5$suggested in \cite{VZ2012} is extended to the case, when there are zeros andpoles of the Green function in momentum space. It is shown how to extend theindex theorem suggested in \cite{VZ2012} to this case. The non - analyticalexceptional points of the Green function appear in the intermediate vacuum,which exists at the transition line between the massive vacua with differentvalues of topological invariants. Their number is related to the jump$\Delta\tilde{\cal N}_4$ across the transition. The given construction isillustrated by momentum space topology of the lattice model with overlapfermions. In the vicinities of the given points the fermion excitations appearthat cannot be considered as usual fermion particles. We, therefore, feel thisappropriate to call them generalized unparticles. This notion is, in generalcase different from the Georgi's unparticle. However, in the case of latticeoverlap fermions the propagator of such excitations is indeed that of thefermionic unparticle suggested in \cite{fermion_unparticle}.