Domain wall junctions are 1/4 BPS states

We study N = 1 SUSY theories in four dimensions with multiple discrete vacua, which admit solitonic solutions describing segments of domain walls meeting at one-dimensional junctions. We show that there exist solutions preserving one-quarter of the underlying supersymmetry-a single Hermitian supercharge. We derive a BPS bound for the masses of these solutions and construct a solution explicitly in a special case. The relevance to the confining phase of N = 1 SUSY Yang-Mills and the M-theory-SYM relationship is discussed.