$\alpha'$-expansion of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM from Fermi Gas

TL;DR

This paper develops a systematic method to compute the large 't Hooft coupling expansion of anti-symmetric Wilson loops in N=4 SYM using Fermi gas techniques, confirming results with recent exact calculations.

Contribution

It introduces a novel application of the Sommerfeld expansion to calculate the α' expansion of Wilson loops in AdS/CFT, linking statistical mechanics methods to string theory computations.

Findings

The expansion matches recent exact results by Fiol and Torrents.

The method provides a systematic way to compute α' corrections in holographic Wilson loops.

Numerical checks validate the accuracy of the expansion.

Abstract

We study the large 't Hooft coupling expansion of 1/2 BPS Wilson loops in the anti-symmetric representation in $ \mathcal{N}=4 $ super Yang-Mills (SYM) theory at the leading order in the 1/N expansion. Via AdS/CFT correspondence, this expansion corresponds to the $\alpha'$ expansion in bulk type IIB string theory. We show that this expansion can be systematically computed by using the low temperature expansion of Fermi distribution function, known as the Sommerfeld expansion in statistical mechanics. We check numerically that our expansion agrees with the exact result of anti-symmetric Wilson loops recently found by Fiol and Torrents.