Equivalence of Wilson loops inN=6super Chern-Simons matter theory andN=4SYM theory

Abstract

In previous investigations, it was found that four-sided polygonal lightlike Wilson loops in $\mathcal{N}=6$ super Chern-Simons matter (ABJM) theory calculated to two-loop order have the same form as the corresponding Wilson loop in $\mathcal{N}=4$ SYM at one-loop order. Here we study lightlike polygonal Wilson loops with $n$ cusps in planar three-dimensional Chern-Simons and ABJM theory to two loops. Remarkably, the result in ABJM theory precisely agrees with the corresponding Wilson loop in $\mathcal{N}=4$ SYM at one-loop order for arbitrary $n$. In particular, anomalous conformal Ward identities allow for a so-called remainder function of conformal cross ratios for $n\ensuremath{\ge}6$, which is found to be trivial at two loops in ABJM theory in the same way as it is trivial in $\mathcal{N}=4$ SYM at one-loop order. Furthermore, the result for arbitrary $n$ obtained here, allows for a further investigation of a Wilson loop/amplitude duality in ABJM theory, for which nontrivial evidence was recently found by a calculation of four-point amplitudes that match the Wilson loop in ABJM theory.