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arXiv · 1405.7444

BPS Soliton Solutions of a D3-brane Action

John H. Schwarz
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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.

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John H. Schwarz. 2014-07-07. BPS Soliton Solutions of a D3-brane Action. https://doi.org/10.1007/jhep07(2014)136

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