Using the WKB expansion for the ABJM matrix model

ABJM Wilson loops in the Fermi gas approach

We present explicit results for the vevs of 1/6 and the 1/2 bps wilson loops, at any winding number, in terms of airy functions.Our expressions are shown to reproduce the low genus results obtained previously in the't hooft expansion.Pacs number(s) : 05.45.+b, 05.70.+k, 11.10.kk, 11.10.gh the matrix model of ab-initio quantum monte carlo (abjm) theory can be formulated in terms of a fermi gas in an external potential.We show that, in this formalism, vevs of wilson loopscorrespond to averages of operators in the statistical-mechanical problem.This makes it possible to calculate these vevs at all orders in 1/n, up to exponentially small corrections, and for arbitrary chern-simons coupling, by using the wkb expansion.