Domain Lines as Fractional Strings

TL;DR

This paper studies domain lines on supersymmetric domain walls in N=2 SQED with two flavors, revealing explicit solutions where these lines confine charges and carry half the bulk flux, connecting bulk and wall physics.

Contribution

It provides explicit solitonic solutions for domain lines on domain walls in N=2 SQED, demonstrating their flux properties and role in charge confinement.

Findings

Domain lines are BPS kinks on the wall world-volume.

They carry half the bulk flux, confining charges on the wall.

Explicit solutions illustrate the confinement mechanism.

Abstract

We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $\beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $\beta=0$ the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase $\sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $\beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines -- string-like objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. We expect that the wall with the domain line on it saturates both the $\{1,0\}$ and the $\{{1/2},{1/2}\}$b central charges of the bulk theory. The domain line carries the magnetic flux which is exactly 1/2 of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov's three-dimensional confinement.