INTERSECTING EXTENDED OBJECTS IN SUPERSYMMETRIC FIELD-THEORIES

We show that there are three cases for which the generic intersections of p-dimensional extended object solutions of a supersymmetric field theory in a d-dimensional space-time are stringlike. They are (i) d = 4, p = 2, (ii) d = 6, p = 3 and (iii) d = 10, p = 5. By consideration of the topological charges associated with these objects we obtain a necessary condition for stable stringlike intersections to occur, a condition that is satisfied by the first two cases but not the third, which may have implications for the "heterotic 5-branes" recently discussed by Strominger. For case (i) we show by an analysis of the d = 4 Wess-Zumino model that stringlike intersections of domain walls can indeed occur.