An Exact Solution of BPS Junctions and Its Properties

TL;DR

This paper presents an exact solution for BPS domain wall junctions in a supersymmetric four-dimensional theory, analyzing their properties, mode equations, and the behavior of Nambu-Goldstone modes, revealing their non-localized nature.

Contribution

It provides the first exact solution for BPS junctions in a simplified N=1 supersymmetric model and studies the properties and behavior of NG modes on these junctions.

Findings

Massless NG modes are non-normalizable and extend infinitely along the wall.

Fermion and boson modes with the same mass form pairs, except for massless modes.

NG fermions exhibit a chiral structure consistent with (1,0) supersymmetry.

Abstract

We have obtained an exact solution for the BPS domain wall junction for a N=1 supersymmetric theory in four dimensions and studied its properties. The model is a simplified version of the N=2 SU(2) gauge theory with N_f=1 broken to N=1 by the mass of the adjoint chiral superfield. We define mode equations and demonstrate explicitly that fermion and boson with the same mass have to come in pairs except massless modes. We work out explicitly massless Nambu-Goldstone (NG) modes on the BPS domain wall junction. We find that their wave functions extend along the wall to infinity (not localized) and are not normalizable. It is argued that this feature is a generic phenomenon of NG modes on domain wall junctions in the bulk flat space in any dimensions. NG fermions exhibit a chiral structure in accordance with unitary representations of (1, 0) supersymmetry algebra where fermion and boson with the same mass come in pairs except massless modes which can appear singly.