  We analyze whether or not Lifshitz field theories in 4 + 1 dimensions may
provide ultraviolet-complete domain-wall brane models. We first show that
Lifshitz scalar field theory can admit topologically stable domain wall
solutions. A Lifshitz fermion field is then added to the toy model, and we
demonstrate that 3+1- dimensional Kaluza-Klein zero mode solutions do not exist
when the four spatial dimensions are treated isotropically. To recover 3 +
1-dimensional chiral fermions dynamically localized to the domain wall, we must
postulate the breaking of full 4-dimensional rotational symmetry down to the
subgroup of rotations which mix the usual 3-dimensional spatial directions and
fix the extra-dimensional axis in addition to the anisotropy between space and
time.
