On 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 $\gamma \gamma$ 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.

Comments: 18 pages, LaTeX, 1 figure. Substantial revision of the text: derivation of the spectra of Kaluza-Klein modes corrected, four-dimensional effective Lagrangians corrected (four-dimensional degrees of freedom missed in the previous versions of the manuscript added), formulas for the amplitudes corrected, figure changed, one reference added, typos corrected