  We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4
Yang-Mills theories. Such states are also realized as three-pronged strings
ending on D3-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 static
electromagnetic force and scalar Higgs force. The instability previously found
in three-pronged string configurations is due to 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 charge. The degeneracy and
the highest spin of the supermultiplet increase linearly with a relative
electric charge. We conclude with comments.

High Energy Physics - Theory