Gauge Theories on the Coulomb branch

TL;DR

This paper constructs a D3-brane world-volume action in AdS5×S5 that models the Coulomb branch of N=4 super Yang-Mills, proposing it as an exact effective action and analyzing BPS solitons representing various charged states.

Contribution

It introduces a conjectured exact effective action for the Coulomb branch and constructs an SL(2,Z) multiplet of BPS solitons within this framework.

Findings

The action reproduces massive states, monopoles, and dyons.

Solitons form spherical 'bubble' phase boundaries.

The model supports SL(2,Z) duality transformations.

Abstract

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.