An exact solution of BPS junctions and its properties

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. T he model is a simplified version of the N = 2 SU(2) gauge theory with N = 1 broken to N = 1 by the mass of the adjoint chiral superfield. We define mo de equations and demonstrate explicitly that fermion and boson with the sam e 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 fin d that their wave functions extend along the wall to infinity (not localize d) and are not normalizable. It is argued that this feature is a generic ph enomenon of NG modes on domain wall junctions in the bulk flat space in any dimensions. NG fermions exhibit a chiral structure in accordance with unit ary representations of (1, 0) supersymmetry algebra where fermion and boson with the same mass come in pairs except massless modes which can appear si ngly. More detailed exposition of our results can be found in Refs.[1], [2] .