1202.2524 (M. A. Zubkov)

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

M. A. Zubkov

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 and
poles of the Green function in momentum space. It is shown how to extend the
index theorem suggested in \cite{VZ2012} to this case. The non - analytical
exceptional points of the Green function appear in the intermediate vacuum,
which exists at the transition line between the massive vacua with different
values of topological invariants. Their number is related to the jump
$\Delta\tilde{\cal N}_4$ across the transition. The given construction is
illustrated by momentum space topology of the lattice model with overlap
fermions. In the vicinities of the given points the fermion excitations appear
that cannot be considered as usual fermion particles. We, therefore, feel this
appropriate to call them generalized unparticles. This notion is, in general
case different from the Georgi's unparticle. However, in the case of lattice
overlap fermions the propagator of such excitations is indeed that of the
fermionic unparticle suggested in \cite{fermion_unparticle}.

View original: http://arxiv.org/abs/1202.2524