Dyons inN=4supersymmetric theories and three-pronged strings

We construct and explore BPS states that preserve $1/4$ of supersymmetry in $N=4\mathrm{}$ Yang-Mills theories. Such states are also realized as three-pronged strings ending on $D3\mathrm{}$-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken Abelian gauge group generators. Generic $1/4$-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between a static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is because of excessive repulsion by one of these static forces. We also present an alternate construction of these $1/4$-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charges. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.