Confinement and Localization on Domain Walls

TL;DR

This paper investigates how U(1) gauge fields localize on domain walls, revealing different phases such as Coulomb or confinement, through models at weak and strong coupling, and compares these with a massless gauge field scenario.

Contribution

It introduces new models demonstrating both Coulomb and confinement phases for gauge fields on domain walls, including an extension of Seiberg--Witten theory and a comparison with a massless gauge field case.

Findings

Gauge fields can be either in Coulomb or confined phases on domain walls.

A simple toy model at weak coupling realizes confinement of charges.

An extended Seiberg--Witten model at strong coupling is analyzed using dual effective action.

Abstract

We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.