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

Understand

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.