Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop

Abstract

Expectation value of lightlike polygon Wilson loop is computed in the three-dimensional ABJM theory up to second-order in `t Hooft coupling in the limit of infinitely many colors and the result is critically compared with that in the four-dimensional N=4 super Yang-Mills theory. We first obtain analytic result for hexagon Wilson loop by combining Mellin-Barnes transformation, high precision numerical computation and the PSLQ algorithm. We then derive a version of operator product expansion (OPE) that reduces lightlike n-gon to a linear combination of (n-2)-gons in the soft-collinear limit of the polygon geometry. The Wilson coefficient of the OPE is the universal antenna function defined by a collapsed lightlike tetragon Wilson loop. Using this, we first construct a all order recursion relation among the lightlike Wilson loops and then solve it for arbitrary polygon with the hexagon Wilson loop as the initial condition. The functional form of the polygon Wilson loop takes the structure remarkably similar to the four-dimensional N=4 super Yang-Mills theory. We also observe that Gram subdeterminant conditions for polygon moduli variables restricts that the Wilson loop contour should be restricted even-sided. As a consistency check, we take thermodynamic limit of regular polygon and reproduce the known results for spacelike circular Wilson loop expectation value.