BPS soliton solutions of a D3-brane action

The world-volume action of a probe D3-brane in AdS(5) x S-5 with N units of flux has the field content, symmetries, and dualities of the U(1) factor of N = 4 U(N + 1) super Yang-Mills theory, spontaneously broken to U(N) x U(1) by being on the Coulomb branch, with the massive fields integrated out. Thus, it might be the exact effective action (a highly effective action), or else a useful approximation to it. We construct an SL(2, Z) multiplet of BPS soliton solutions of the D3-brane action and show that in the N = 1 case they correspond to the electrically charged states that have been integrated out as well as magnetic monopoles and dyons. Their charges are uniformly spread on a spherical surface, a soliton bubble, which can be interpreted as a phase boundary. This picture is consistent with previous results in the string theory and field theory literature.