  The domain wall fermion formalism in lattice gauge theory is much
investigated recently. This is set up by reducing 4+1 dimensional theory to low
energy effective 4 dimensional one. In order to look around other possibilities
of realizing chiral fermion on the lattice, we construct vortex fermion by
reducing 4+2 dimensional theory to low energy effective 4 dimensional one on
the lattice. In extra 2 dimensions we propose a new lattice regularization
which has a discrete rotational invariance but not a translational one. In
order to eliminate doubling species in the naive construction we introduce the
extended Wilson term which is appropriate to our model. We propose two models
for convenience and show that a normalizable zero mode solution appears at the
core of the vortex.
