Domain Wall Junction in N=2 Supersymmetric QED in four dimensions

TL;DR

This work constructs an exact analytic domain-wall junction in four-dimensional $N=2$ SUSY QED with three massive hypermultiplets, showing the configuration preserves $rac{1}{4}$ of the original eight supercharges. The authors derive the BPS equations as minimum-energy conditions and realize an explicit $Z_3$-symmetric junction by tuning the FI and mass parameters, with exact field profiles for the hypermultiplets and the neutral scalar. The solution exhibits translational and global $U(1)$ zero modes and a rich spectrum of Nambu-Goldstone bosons/fermions, while many SUSY modes remain nonnormalizable on the junction. A detailed account of the eight SUSY transformations is provided, and the construction is connected to five-dimensional theories via dimensional reduction, clarifying when and how complex masses in 4D arise from higher-dimensional origins. The results illuminate the interplay between FI terms, complex masses, and BPS junctions in ${N}=2$ theories and offer a concrete bridge to higher-dimensional model-building scenarios.

Abstract

An exact solution of domain wall junction is obtained in N=2 supersymmetric (SUSY) QED with three massive hypermultiplets. The junction preserves two out of eight SUSY. Both a (magnetic) Fayet-Iliopoulos (FI) term and complex masses for hypermultiplets are needed to obtain the junction solution. There are zero modes corresponding to spontaneously broken translation, SUSY, and U(1). All broken and unbroken SUSY charges are explicitly worked out in the Wess-Zumino gauge in N=1 superfields as well as in components. The relation to models in five dimensions is also clarified.

Figures (6)

• Figure 1: Vacua in complex $\phi$ plane.
• Figure 2: The $Z_3$ junction in real space $z=x^1+ix^2$.
• Figure 3: Along $z\to +\infty$ one obtains the vacuum $3$, where only $q_3$ takes non-zero values. Along $z\to -\infty$ one obtains the middle point of wall between first and second vacua, where $|q_1|=|q_2|$.
• Figure 4: Energy density of the $Z_3$ junction configuration of ${\cal N}=2$ SUSY QED.
• Figure 5: The transformation laws for vector multiplet