Holographic description of D3-branes in flat space

TL;DR

This paper constructs a holographic dual for D3-branes in flat space by embedding into a large anti-de Sitter space, revealing how boundary gauge theory encodes the brane geometry's detailed structure.

Contribution

It introduces a scheme to realize the full D3-brane geometry holographically within a multi-center AdS space, extending the holographic energy-distance relation.

Findings

The D3-brane geometry size scales as (K/N)^{1/4} U^0.

The energy-scale relation becomes U-independent in a specific radial range.

Boundary gauge theory encodes detailed D3-brane structure at the Higgs scale.

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.