Wilson Loops as D3-Branes

TL;DR

This paper demonstrates that half-BPS Wilson loops in N=4 SYM, in various representations, can be described by D3-brane configurations in AdS_5xS^5, providing a concrete bulk dual for these operators.

Contribution

It establishes the explicit correspondence between Wilson loops in arbitrary representations and D3-brane configurations in the AdS/CFT framework.

Findings

D3-brane configurations correspond to Wilson loops in symmetric representations.

Explicit integration of D3-brane degrees of freedom reproduces the Wilson loop operators.

The bulk description applies to arbitrary representations of the gauge group.

Abstract

We prove that the half-BPS Wilson loop operator of N=4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS_5xS^5, as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrated by explicitly integrating out the degrees of freedom on the D3-branes and showing that they insert a half-BPS Wilson loop operator into the N=4 SYM path integral in the desired representation.