Domain-wall branes in Lifshitz theories

Abstract

We analyze whether or not Lifshitz field theories in 4 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 3dimensional Kaluza-Klein zero-mode solutions do not exist when the four spatial dimensions are treated isotropically. To recover 3dimensional 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 ..