α′-expansion of antisymmetric Wilson loops in N = 4 SYM from Fermi gas

Abstract

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