A version of softly broken N velence 2 supersymmetric quantum electrodynamics(SQED) with 2 flavors is considered. A Fayet-Iliopoulos parameter and a mass term beta which breaks the extended supersymmetry down to N velence 1 are added. The bulk theory has two vacua; at beta velence 0 the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase a 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. The domain line carries a 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.
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