Antisymmetric Wilson loops in $\mathcal{N}=4$ SYM beyond the planar limit

TL;DR

This paper analyzes antisymmetric Wilson loops in N=4 SYM beyond the planar limit, computing 1/N corrections via matrix model techniques and highlighting discrepancies with holographic dual predictions.

Contribution

It provides the first calculation of 1/N corrections for antisymmetric Wilson loops in N=4 SYM using matrix model loop equations.

Findings

Computed 1/N correction at leading order in 't Hooft coupling.

Found disagreement with holographic D5-brane effective action.

Indicates gravitational backreaction effects are important.

Abstract

We study the $\frac{1}{2}$-BPS circular Wilson loop in the totally antisymmetric representation of the gauge group in $\mathcal N =4 $ supersymmetric Yang-Mills. This observable is captured by a Gaussian matrix model with appropriate insertion. We compute the first $1/N$ correction at leading order in 't Hooft coupling by means of the matrix model loop equations. Disagreement with the 1-loop effective action of the holographically dual $D5$-brane suggests the need to account for gravitational backreaction on the string theory side.