Approach to the arbitrariness problem of boundary conditions in $S^1/Z_2$ brane-world models

TL;DR

This paper investigates the boundary condition arbitrariness in $S^1/Z_2$ brane-world models with gauge group $U(N)$, showing how gauge transformations relate different BCs and resolving arbitrariness on the bulk and IR-brane.

Contribution

It demonstrates that gauge transformations can connect various boundary conditions, reducing arbitrariness except at the UV-brane, providing a clearer understanding of boundary condition equivalences in these models.

Findings

Equivalent BCs are connected via gauge transformations on the UV-brane.

A kink gauge transformation links all BCs on the bulk and IR-brane.

Arbitrariness of BCs is resolved on the bulk and IR-brane, but not on the UV-brane.

Abstract

We study the arbitrariness of boundary conditions (BCs) on $S^1/Z_2$ brane-world models with the gauge group $U(N)$. The BCs are chosen independently on the branes and the bulk in this model. There are numerous choices for BCs in general, but some of the BCs are connected through gauge transformations. We show that the equivalent relations are obtained on the UV-brane without relying on specific transformation parameters. There is no other equivalent relation on the UV-brane. On the other hand, we find that a gauge transformation with a kink connects all the BCs on the bulk and IR-brane. It means that the arbitrariness of BCs is completely solved on the bulk and the IR-brane except for the UV-brane.