BPS Soliton Solutions of a D3-brane Action

TL;DR

This paper constructs and analyzes BPS soliton solutions in the D3-brane action within an $AdS_5 imes S^5$ background, revealing their interpretation as phase boundaries and their relation to known string and field theory states.

Contribution

It introduces an $SL(2,Z)$ multiplet of BPS solitons in the D3-brane action, linking them to electric, magnetic, and dyonic states, and interprets their charge distribution as a phase boundary.

Findings

Solitons form spherical charge distributions called bubbles.

Solutions correspond to known string theory states like monopoles and dyons.

Results align with previous string and field theory literature.

Abstract

The world-volume action of a probe D3-brane in $AdS_5 \times S^5$ with $N$ units of flux 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. 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.