Gauge Theories on the Coulomb branch

We construct the world-volume action of a probe D3-brane in AdS_5×S^5 with N units of flux. It 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)×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 they reproduce 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.