  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.
