TL;DR
This paper investigates a five-dimensional brane world model with localized gauge fields, revealing that certain process amplitudes diverge in the infinite extra dimension limit, indicating a potential fundamental issue in such models.
Contribution
It introduces a toy model with fermions and localized electromagnetic fields on a brane, analyzing divergences in the effective four-dimensional theory as the extra dimension becomes infinite.
Findings
Lowest-order process amplitudes diverge in the infinite extra dimension limit.
The divergence suggests a fundamental problem called 'localization catastrophe' in brane models.
The results imply potential limitations for realistic brane world scenarios with infinite extra dimensions.
Abstract
In this paper a model in a space-time with compact extra dimension is presented, describing five-dimensional fermion fields interacting with an electromagnetic field localized on a brane. This model can be considered as a toy model for examining possible consequences of the localization of gauge fields on a brane. It is shown that in the limit of infinite extra dimension, the lowest-order amplitudes of some processes in the resulting four-dimensional effective theory are divergent. Such a "localization catastrophe" can be inherent to more realistic brane world models with infinite extra dimensions.
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