Localized Gauge Multiplet on a Wall

TL;DR

This paper investigates how vector multiplets can be localized on a BPS wall in a supersymmetric U(1) gauge theory, revealing that the vector field becomes confined to the wall with a mass inversely proportional to the wall's width.

Contribution

It provides an explicit model demonstrating the localization of gauge fields on a wall in four-dimensional supersymmetric theories, including a non-supersymmetric five-dimensional extension.

Findings

Vector multiplets localize on BPS walls in the model.

The localized vector field's mass is inversely proportional to the wall width.

The model offers an explicit example of gauge field localization phenomena.

Abstract

The localization of vector multiplets is examined using the {\cal N}=1 supersymmetric U(1) gauge theory with the Fayet-Iliopoulos term coupled to charged chiral multiplets in four dimensions. The vector field becomes localized on a BPS wall connecting two different vacua that break the gauge symmetry. The vacuum expectation values of charged fields vanish (approximately) around the center of the wall, causing the Higgs mechanism to be ineffective. The mass of the localized vector multiplet is found to be the inverse width of the wall. The model gives an explicit example of this general phenomenon. A five-dimensional version of the model can also be constructed if we abandon supersymmetry.