  We construct the world-volume action of a probe D3-brane in $AdS_5 \times
S^5$ with $N$ units of flux. It has the field content, symmetries, and
dualities of the $U(1)$ factor of ${\cal N} =4$ $U(N+1)$ super Yang--Mills
theory, spontaneously broken to $U(N) \times U(1)$ by being on the Coulomb
branch, with the massive fields integrated out. This motivates the conjecture
that it is the exact effective action, called a `highly effective action'
(HEA). We construct an $SL(2,Z)$ multiplet of BPS soliton solutions of the
D3-brane theory (the conjectured HEA) and show that it reproduces the
electrically charged massive states that have been integrated out as well as
magnetic monopoles and dyons. Their charges are uniformly spread on a spherical
surface, called a `soliton bubble', which is interpreted as a phase boundary.
