Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory

TL;DR

This paper demonstrates that light-like polygonal Wilson loops in ABJM theory at two loops match the one-loop results in N=4 SYM for any number of cusps, revealing a deep equivalence and supporting a Wilson loop/amplitude duality in ABJM.

Contribution

It shows the equivalence of Wilson loops in ABJM and N=4 SYM at different loop orders and extends the understanding of Wilson loop/amplitude duality in ABJM theory.

Findings

Wilson loops in ABJM at two loops match N=4 SYM at one loop for any n

The conformal remainder function is trivial at two loops in ABJM

Evidence supports Wilson loop/amplitude duality in ABJM theory

Abstract

In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study light-like 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 N = 4 SYM at one-loop order for arbitrary n. In particular, anomalous conformal Ward identites allow for a so-called remainder function of conformal cross ratios, which is found to be trivial at two loops in ABJM theory in the same way as it is trivial in 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 non-trivial evidence was recently found by a calculation of four-point amplitudes that match the Wilson loop in ABJM theory.