String webs and 1/4 BPS monopoles

We argue for the existence of many new 1/4 BPS states in N = 4 SU(N-c) Supe r-Yang-Mills theory with N-c greater than or equal to 3, by constructing th em from supersymmetric string webs whose external strings terminate on para llel D3-branes. The masses of the string webs are shown to agree with the B PS bound for the corresponding states in SYM. We identify the curves of mar ginal stability, at which these states decay into other BPS states. We find the bosonic and fermionic zero-modes of the string webs, and thereby the d egeneracy and spin content of some of the BPS states. States of arbitrarily high spin are predicted in this manner, all of which become massless at th e conformal point. For N-c greater than or equal to 4 we find BPS states wh ich transform in long multiplets, and are therefore not protected against b ecoming stable non-BPS states as moduli are varied. The mass of these extre mal non-BPS states is constrained as they are connected to BPS states. Anal ogous geometric phenomena are anticipated. (C) 1999 Elsevier Science B.V.