# Revisiting instabilities of $S^1/Z_2$ models with loop-induced Fayet-Iliopoulos terms

## TL;DR

This paper examines the stability of 5D supersymmetric $U(1)$ models on $S^1/Z_2$, focusing on loop-induced Fayet-Iliopoulos terms and their impact on vacuum stability, revealing conditions for stable configurations.

## Contribution

It provides a detailed analysis of how loop-induced FI-terms affect vacuum stability in 5D models, highlighting the role of matter wave functions in this process.

## Key findings

- Localized FI-terms depend on matter wave functions
- Vacuum stability requires bulk zero modes to shield brane charge
- Stable configurations are achieved when conditions on wave functions are met

## Abstract

We study Fayet-Iliopoulos (FI) terms of 5-dimensional supersymmetric $U(1)$ gauge theory compactified on $S^1/Z_2$. In this model, loop diagrams including matter hypermultiplets and brane chiral multiplets induce FI-terms localized at the fixed points. Localized FI-terms lead instabilities of bulk modes. The form of the induced FI-terms strictly depends on wave function profiles of matter multiplets. It is a non-trivial question whether the vacuum of 1-loop corrected potential is stable under radiative corrections. We investigate this issue and it is found that the stable configuration is obtained when the bulk zero modes shield the brane charge completely.