Domain-wall branes in Lifshitz theories

TL;DR

This paper investigates Lifshitz field theories in 4+1 dimensions for their potential to create ultraviolet-complete domain-wall brane models, analyzing scalar and fermion fields and the conditions for localizing chiral fermions.

Contribution

It demonstrates that Lifshitz scalar theories can have stable domain walls and explores the conditions under which fermions can be localized on these walls, highlighting the necessity of symmetry breaking.

Findings

Lifshitz scalar fields admit topologically stable domain walls.

Isotropic Lifshitz fermions do not produce localized zero modes.

Breaking rotational symmetry enables chiral fermion localization.

Abstract

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.