Holographic description of D3-branes in flat space

Abstract

We describe a scheme for constructing the holographic dual of the full D3-brane geometry with charge $K$ by embedding it into a large anti-de Sitter space of size $N$. Such a geometry is realized in a multi-center anti-de Sitter geometry which admits a simple field theory interpretation as $SU(N+K)$ gauge theory broken to $SU(N)\times SU(K)$. We find that the characteristic size of the D3-brane geometry is of order $(K/N{)}^{1/4}{U}^0$ where $U^0$ is the scale of the Higgs. By choosing $N$ to be much larger than $K$, the scale of the D3-brane metric can be well separated from the Higgs scale in the radial coordinate. We generalize the holographic energy-distance relation and estimate the characteristic energy scale associated with these radial scales, and find that the $E/U$ relation becomes effectively $U$ independent in the range $(K/N{)}^{1/2}{U}^0<U<U^0$. This implies that all detailed structure of the D3-brane geometry is encoded in the fine structure of the boundary gauge theory at around the Higgs scale.

8 pages, 1 eps figure

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