Gauge Theories on the Coulomb branch

Understand

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.