Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-03-26
Phys.Rev. D60 (1999) 127902
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, 1 eps figure
Scientific paper
10.1103/PhysRevD.60.127902
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.
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