On unremovable divergencies in four-dimensional electrodynamics localized on a domain wall

TL;DR

This paper demonstrates that in a model with fermions and gauge fields localized on a domain wall, the four-dimensional effective electrodynamics exhibits unavoidable divergences in elastic photon scattering, challenging its viability.

Contribution

It reveals that higher modes induce divergences in the effective theory, showing a fundamental limitation in localizing fields on a domain wall.

Findings

Divergences in elastic gamma-gamma scattering amplitude

Higher modes contribute to non-renormalizable divergences

Localization scenario cannot be considered realistic due to divergences

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.