Domain wall junctions are 1/4 BPS states

Abstract

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.