Unremovable divergencies in four-dimensional electrodynamics localized on a domain wall

Abstract

In this paper a model describing fermions and gauge field localized on a domain wall is considered. The zero-mode sector of the model reproduces four-dimensional spinor electrodynamics. It is shown that in the resulting four-dimensional effective theory the lowest-order renormalized amplitude of the elastic $\ensuremath{\gamma}\ensuremath{\gamma}$ scattering process is divergent due to the contributions of higher modes and thus such a scenario can not be considered as a realistic mechanism for fields localization on a domain wall.