Differential Equations for Wilson Loops in ABJM Theory

Abstract

We derive a system of differential equations which are satisfied by the vevs of BPS Wilson loops and 't Hooft coupling of ABJM theory. They are Picard-Fuchs equations of an algebraic curve defined by the derivative of the planar resolvent of the corresponding matrix model. The weak and strong coupling behaviors can be reproduced by their local solutions around regular singularities. We also obtain a recursion relation which can be used to determine the planar vevs of BPS Wilson loops in arbitrary representations.