On the D3-brane description of some 1/4 BPS Wilson loops

TL;DR

This paper constructs D3-brane solutions for certain 1/4 BPS Wilson loops in N=4 SYM, extending the D-brane description beyond the previously known half-BPS cases, and matches their expectation values with matrix model predictions.

Contribution

It provides explicit D3-brane solutions for 1/4 BPS Wilson loops, demonstrating agreement with matrix model calculations and exploring stability properties.

Findings

D3-brane solutions for 1/4 BPS loops are found.

The brane action reproduces Wilson loop expectation values including 1/N corrections.

Two classical solutions are identified, with one unstable solution contributing negligible corrections.

Abstract

Recently it has been proposed that Wilson loops in high-dimensional representations in N=4 supersymmetric Yang-Mills theory (or multiply wrapped loops) are described by D-branes in AdS_5 x S^5, rather than by fundamental strings. Thus far explicit D3-brane solutions have been only found in the case of the half-BPS circle or line. Here we present D3-brane solutions describing some 1/4 BPS loops. In one case, where the loop is conjectured to be given by a Gaussian matrix model, the action of the brane correctly reproduces the expectation value of the Wilson loop including all 1/N corrections at large \lambda. As in the corresponding string solution, here too we find two classical solutions, one stable and one not. The unstable one contributes exponentially small corrections that agree with the matrix model calculation.