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.

• Received 21 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.116007