Modeling a network of brane worlds

We study junctions of supersymmetric domain walls in N = 1 supergravity the ories in four dimensions, coupled to a chiral superfield with quartic super potential having Z(3) symmetry. After deriving a BPS equation of the domain wall junction, we consider a stable hexagonal configuration of network of brane junctions, which are only approximately locally BPS. We propose a mod el for a mechanism of supersymmetry breaking without loss of stability, whe re a messenger for the SUSY breaking comes from the neighboring anti-BPS ju nction world, propagating along the domain walls connection them.